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Balancing Sample Efficiency and Suboptimality in Inverse Reinforcement Learning | null | We propose a novel formulation for the Inverse Reinforcement Learning (IRL) problem, which jointly accounts for the compatibility with the expert behavior of the identified reward and its effectiveness for the subsequent forward learning phase. Albeit quite natural, especially when the final goal is apprenticeship learning (learning policies from an expert), this aspect has been completely overlooked by IRL approaches so far. We propose a new model-free IRL method that is remarkably able to autonomously find a trade-off between the error induced on the learned policy when potentially choosing a sub-optimal reward, and the estimation error caused by using finite samples in the forward learning phase, which can be controlled by explicitly optimizing also the discount factor of the related learning problem. The approach is based on a min-max formulation for the robust selection of the reward parameters and the discount factor so that the distance between the expert’s policy and the learned policy is minimized in the successive forward learning task when a finite and possibly small number of samples is available. Differently from the majority of other IRL techniques, our approach does not involve any planning or forward Reinforcement Learning problems to be solved. After presenting the formulation, we provide a numerical scheme for the optimization, and we show its effectiveness on an illustrative numerical case. | Angelo Damiani, Giorgio Manganini, Alberto Maria Metelli, Marcello Restelli | null | null | 2,022 | icml |
Unsupervised Image Representation Learning with Deep Latent Particles | null | We propose a new representation of visual data that disentangles object position from appearance. Our method, termed Deep Latent Particles (DLP), decomposes the visual input into low-dimensional latent “particles”, where each particle is described by its spatial location and features of its surrounding region. To drive learning of such representations, we follow a VAE-based based approach and introduce a prior for particle positions based on a spatial-Softmax architecture, and a modification of the evidence lower bound loss inspired by the Chamfer distance between particles. We demonstrate that our DLP representations are useful for downstream tasks such as unsupervised keypoint (KP) detection, image manipulation, and video prediction for scenes composed of multiple dynamic objects. In addition, we show that our probabilistic interpretation of the problem naturally provides uncertainty estimates for particle locations, which can be used for model selection, among other tasks. | Tal Daniel, Aviv Tamar | null | null | 2,022 | icml |
Guarantees for Epsilon-Greedy Reinforcement Learning with Function Approximation | null | Myopic exploration policies such as epsilon-greedy, softmax, or Gaussian noise fail to explore efficiently in some reinforcement learning tasks and yet, they perform well in many others. In fact, in practice, they are often selected as the top choices, due to their simplicity. But, for what tasks do such policies succeed? Can we give theoretical guarantees for their favorable performance? These crucial questions have been scarcely investigated, despite the prominent practical importance of these policies. This paper presents a theoretical analysis of such policies and provides the first regret and sample-complexity bounds for reinforcement learning with myopic exploration. Our results apply to value-function-based algorithms in episodic MDPs with bounded Bellman Eluder dimension. We propose a new complexity measure called myopic exploration gap, denoted by alpha, that captures a structural property of the MDP, the exploration policy and the given value function class. We show that the sample-complexity of myopic exploration scales quadratically with the inverse of this quantity, 1 / alpha^2. We further demonstrate through concrete examples that myopic exploration gap is indeed favorable in several tasks where myopic exploration succeeds, due to the corresponding dynamics and reward structure. | Chris Dann, Yishay Mansour, Mehryar Mohri, Ayush Sekhari, Karthik Sridharan | null | null | 2,022 | icml |
DisPFL: Towards Communication-Efficient Personalized Federated Learning via Decentralized Sparse Training | null | Personalized federated learning is proposed to handle the data heterogeneity problem amongst clients by learning dedicated tailored local models for each user. However, existing works are often built in a centralized way, leading to high communication pressure and high vulnerability when a failure or an attack on the central server occurs. In this work, we propose a novel personalized federated learning framework in a decentralized (peer-to-peer) communication protocol named DisPFL, which employs personalized sparse masks to customize sparse local models on the edge. To further save the communication and computation cost, we propose a decentralized sparse training technique, which means that each local model in DisPFL only maintains a fixed number of active parameters throughout the whole local training and peer-to-peer communication process. Comprehensive experiments demonstrate that DisPFL significantly saves the communication bottleneck for the busiest node among all clients and, at the same time, achieves higher model accuracy with less computation cost and communication rounds. Furthermore, we demonstrate that our method can easily adapt to heterogeneous local clients with varying computation complexities and achieves better personalized performances. | Rong Dai, Li Shen, Fengxiang He, Xinmei Tian, Dacheng Tao | null | null | 2,022 | icml |
Robust Multi-Objective Bayesian Optimization Under Input Noise | null | Bayesian optimization (BO) is a sample-efficient approach for tuning design parameters to optimize expensive-to-evaluate, black-box performance metrics. In many manufacturing processes, the design parameters are subject to random input noise, resulting in a product that is often less performant than expected. Although BO methods have been proposed for optimizing a single objective under input noise, no existing method addresses the practical scenario where there are multiple objectives that are sensitive to input perturbations. In this work, we propose the first multi-objective BO method that is robust to input noise. We formalize our goal as optimizing the multivariate value-at-risk (MVaR), a risk measure of the uncertain objectives. Since directly optimizing MVaR is computationally infeasible in many settings, we propose a scalable, theoretically-grounded approach for optimizing MVaR using random scalarizations. Empirically, we find that our approach significantly outperforms alternative methods and efficiently identifies optimal robust designs that will satisfy specifications across multiple metrics with high probability. | Samuel Daulton, Sait Cakmak, Maximilian Balandat, Michael A. Osborne, Enlu Zhou, Eytan Bakshy | null | null | 2,022 | icml |
Dialog Inpainting: Turning Documents into Dialogs | null | Many important questions (e.g. "How to eat healthier?") require conversation to establish context and explore in depth. However, conversational question answering (ConvQA) systems have long been stymied by scarce training data that is expensive to collect. To address this problem, we propose a new technique for synthetically generating diverse and high-quality dialog data: dialog inpainting. Our approach takes the text of any document and transforms it into a two-person dialog between the writer and an imagined reader: we treat sentences from the article as utterances spoken by the writer, and then use a dialog inpainter to predict what the imagined reader asked or said in between each of the writer’s utterances. By applying this approach to passages from Wikipedia and the web, we produce WikiDialog and WebDialog, two datasets totalling 19 million diverse information-seeking dialogs – 1,000x larger than the largest existing ConvQA dataset. Furthermore, human raters judge the answer adequacy and conversationality of WikiDialog to be as good or better than existing manually-collected datasets. Remarkably, our approach shows strong zero-shot capability, generating high quality synthetic data without using any in-domain ConvQA data. Using our inpainted data to pre-train ConvQA retrieval systems, we significantly advance state-of-the-art across three benchmarks (QReCC, OR-QuAC, TREC CAsT) yielding up to 40% relative gains on standard evaluation metrics. | Zhuyun Dai, Arun Tejasvi Chaganty, Vincent Y Zhao, Aida Amini, Qazi Mamunur Rashid, Mike Green, Kelvin Guu | null | null | 2,022 | icml |
Monarch: Expressive Structured Matrices for Efficient and Accurate Training | null | Large neural networks excel in many domains, but they are expensive to train and fine-tune. A popular approach to reduce their compute or memory requirements is to replace dense weight matrices with structured ones (e.g., sparse, low-rank, Fourier transform). These methods have not seen widespread adoption (1) in end-to-end training due to unfavorable efficiency–quality tradeoffs, and (2) in dense-to-sparse fine-tuning due to lack of tractable algorithms to approximate a given dense weight matrix. To address these issues, we propose a class of matrices (Monarch) that is hardware-efficient (they are parameterized as products of two block-diagonal matrices for better hardware utilization) and expressive (they can represent many commonly used transforms). Surprisingly, the problem of approximating a dense weight matrix with a Monarch matrix, though nonconvex, has an analytical optimal solution. These properties of Monarch matrices unlock new ways to train and fine-tune sparse and dense models. We empirically validate that Monarch can achieve favorable accuracy-efficiency tradeoffs in several end-to-end sparse training applications: speeding up ViT and GPT-2 training on ImageNet classification and Wikitext-103 language modeling by 2x with comparable model quality, and reducing the error on PDE solving and MRI reconstruction tasks by 40%. In sparse-to-dense training, with a simple technique called "reverse sparsification," Monarch matrices serve as a useful intermediate representation to speed up GPT-2 pretraining on OpenWebText by 2x without quality drop. The same technique brings 23% faster BERT pretraining than even the very optimized implementation from Nvidia that set the MLPerf 1.1 record. In dense-to-sparse fine-tuning, as a proof-of-concept, our Monarch approximation algorithm speeds up BERT fine-tuning on GLUE by 1.7x with comparable accuracy. | Tri Dao, Beidi Chen, Nimit S Sohoni, Arjun Desai, Michael Poli, Jessica Grogan, Alexander Liu, Aniruddh Rao, Atri Rudra, Christopher Re | null | null | 2,022 | icml |
Framework for Evaluating Faithfulness of Local Explanations | null | We study the faithfulness of an explanation system to the underlying prediction model. We show that this can be captured by two properties, consistency and sufficiency, and introduce quantitative measures of the extent to which these hold. Interestingly, these measures depend on the test-time data distribution. For a variety of existing explanation systems, such as anchors, we analytically study these quantities. We also provide estimators and sample complexity bounds for empirically determining the faithfulness of black-box explanation systems. Finally, we experimentally validate the new properties and estimators. | Sanjoy Dasgupta, Nave Frost, Michal Moshkovitz | null | null | 2,022 | icml |
DreamerPro: Reconstruction-Free Model-Based Reinforcement Learning with Prototypical Representations | null | Reconstruction-based Model-Based Reinforcement Learning (MBRL) agents, such as Dreamer, often fail to discard task-irrelevant visual distractions that are prevalent in natural scenes. In this paper, we propose a reconstruction-free MBRL agent, called DreamerPro, that can enhance robustness to distractions. Motivated by the recent success of prototypical representations, a non-contrastive self-supervised learning approach in computer vision, DreamerPro combines Dreamer with prototypes. In order for the prototypes to benefit temporal dynamics learning in MBRL, we propose to additionally learn the prototypes from the recurrent states of the world model, thereby distilling temporal structures from past observations and actions into the prototypes. Experiments on the DeepMind Control suite show that DreamerPro achieves better overall performance than state-of-the-art contrastive MBRL agents when there are complex background distractions, and maintains similar performance as Dreamer in standard tasks where contrastive MBRL agents can perform much worse. | Fei Deng, Ingook Jang, Sungjin Ahn | null | null | 2,022 | icml |
Adversarial Vulnerability of Randomized Ensembles | null | Despite the tremendous success of deep neural networks across various tasks, their vulnerability to imperceptible adversarial perturbations has hindered their deployment in the real world. Recently, works on randomized ensembles have empirically demonstrated significant improvements in adversarial robustness over standard adversarially trained (AT) models with minimal computational overhead, making them a promising solution for safety-critical resource-constrained applications. However, this impressive performance raises the question: Are these robustness gains provided by randomized ensembles real? In this work we address this question both theoretically and empirically. We first establish theoretically that commonly employed robustness evaluation methods such as adaptive PGD provide a false sense of security in this setting. Subsequently, we propose a theoretically-sound and efficient adversarial attack algorithm (ARC) capable of compromising random ensembles even in cases where adaptive PGD fails to do so. We conduct comprehensive experiments across a variety of network architectures, training schemes, datasets, and norms to support our claims, and empirically establish that randomized ensembles are in fact more vulnerable to $\ell_p$-bounded adversarial perturbations than even standard AT models. Our code can be found at https://github.com/hsndbk4/ARC. | Hassan Dbouk, Naresh Shanbhag | null | null | 2,022 | icml |
Deep Causal Metric Learning | null | Deep metric learning aims to learn distance metrics that measure similarities and dissimilarities between samples. The existing approaches typically focus on designing different hard sample mining or distance margin strategies and then minimize a pair/triplet-based or proxy-based loss over the training data. However, this can lead the model to recklessly learn all the correlated distances found in training data including the spurious distance (e.g., background differences) that is not the distance of interest and can harm the generalization of the learned metric. To address this issue, we study metric learning from a causality perspective and accordingly propose deep causal metric learning (DCML) that pursues the true causality of the distance between samples. DCML is achieved through explicitly learning environment-invariant attention and task-invariant embedding based on causal inference. Extensive experiments on several benchmark datasets demonstrate the superiority of DCML over the existing methods. | Xiang Deng, Zhongfei Zhang | null | null | 2,022 | icml |
Understanding Doubly Stochastic Clustering | null | The problem of projecting a matrix onto the space of doubly stochastic matrices finds several applications in machine learning. For example, in spectral clustering, it has been shown that forming the normalized Laplacian matrix from a data affinity matrix has close connections to projecting it onto the set of doubly stochastic matrices. However, the analysis of why this projection improves clustering has been limited. In this paper we present theoretical conditions on the given affinity matrix under which its doubly stochastic projection is an ideal affinity matrix (i.e., it has no false connections between clusters, and is well-connected within each cluster). In particular, we show that a necessary and sufficient condition for a projected affinity matrix to be ideal reduces to a set of conditions on the input affinity that decompose along each cluster. Further, in the subspace clustering problem, where each cluster is defined by a linear subspace, we provide geometric conditions on the underlying subspaces which guarantee correct clustering via a continuous version of the problem. This allows us to explain theoretically the remarkable performance of a recently proposed doubly stochastic subspace clustering method. | Tianjiao Ding, Derek Lim, Rene Vidal, Benjamin D Haeffele | null | null | 2,022 | icml |
Born-Infeld (BI) for AI: Energy-Conserving Descent (ECD) for Optimization | null | We introduce a novel framework for optimization based on energy-conserving Hamiltonian dynamics in a strongly mixing (chaotic) regime and establish its key properties analytically and numerically. The prototype is a discretization of Born-Infeld dynamics, with a squared relativistic speed limit depending on the objective function. This class of frictionless, energy-conserving optimizers proceeds unobstructed until slowing naturally near the minimal loss, which dominates the phase space volume of the system. Building from studies of chaotic systems such as dynamical billiards, we formulate a specific algorithm with good performance on machine learning and PDE-solving tasks, including generalization. It cannot stop at a high local minimum, an advantage in non-convex loss functions, and proceeds faster than GD+momentum in shallow valleys. | Giuseppe Bruno De Luca, Eva Silverstein | null | null | 2,022 | icml |
NeuralEF: Deconstructing Kernels by Deep Neural Networks | null | Learning the principal eigenfunctions of an integral operator defined by a kernel and a data distribution is at the core of many machine learning problems. Traditional nonparametric solutions based on the Nystrom formula suffer from scalability issues. Recent work has resorted to a parametric approach, i.e., training neural networks to approximate the eigenfunctions. However, the existing method relies on an expensive orthogonalization step and is difficult to implement. We show that these problems can be fixed by using a new series of objective functions that generalizes the EigenGame to function space. We test our method on a variety of supervised and unsupervised learning problems and show it provides accurate approximations to the eigenfunctions of polynomial, radial basis, neural network Gaussian process, and neural tangent kernels. Finally, we demonstrate our method can scale up linearised Laplace approximation of deep neural networks to modern image classification datasets through approximating the Gauss-Newton matrix. Code is available at https://github.com/thudzj/neuraleigenfunction. | Zhijie Deng, Jiaxin Shi, Jun Zhu | null | null | 2,022 | icml |
Bayesian Learning with Information Gain Provably Bounds Risk for a Robust Adversarial Defense | null | We present a new algorithm to learn a deep neural network model robust against adversarial attacks. Previous algorithms demonstrate an adversarially trained Bayesian Neural Network (BNN) provides improved robustness. We recognize the learning approach for approximating the multi-modal posterior distribution of an adversarially trained Bayesian model can lead to mode collapse; consequently, the model’s achievements in robustness and performance are sub-optimal. Instead, we first propose preventing mode collapse to better approximate the multi-modal posterior distribution. Second, based on the intuition that a robust model should ignore perturbations and only consider the informative content of the input, we conceptualize and formulate an information gain objective to measure and force the information learned from both benign and adversarial training instances to be similar. Importantly. we prove and demonstrate that minimizing the information gain objective allows the adversarial risk to approach the conventional empirical risk. We believe our efforts provide a step towards a basis for a principled method of adversarially training BNNs. Our extensive experimental results demonstrate significantly improved robustness up to 20% compared with adversarial training and Adv-BNN under PGD attacks with 0.035 distortion on both CIFAR-10 and STL-10 dataset. | Bao Gia Doan, Ehsan M. Abbasnejad, Javen Qinfeng Shi, Damith C. Ranasinghe | null | null | 2,022 | icml |
Distinguishing rule and exemplar-based generalization in learning systems | null | Machine learning systems often do not share the same inductive biases as humans and, as a result, extrapolate or generalize in ways that are inconsistent with our expectations. The trade-off between exemplar- and rule-based generalization has been studied extensively in cognitive psychology; in this work, we present a protocol inspired by these experimental approaches to probe the inductive biases that control this trade-off in category-learning systems such as artificial neural networks. We isolate two such inductive biases: feature-level bias (differences in which features are more readily learned) and exemplar-vs-rule bias (differences in how these learned features are used for generalization of category labels). We find that standard neural network models are feature-biased and have a propensity towards exemplar-based extrapolation; we discuss the implications of these findings for machine-learning research on data augmentation, fairness, and systematic generalization. | Ishita Dasgupta, Erin Grant, Tom Griffiths | null | null | 2,022 | icml |
Analysis of Stochastic Processes through Replay Buffers | null | Replay buffers are a key component in many reinforcement learning schemes. Yet, their theoretical properties are not fully understood. In this paper we analyze a system where a stochastic process X is pushed into a replay buffer and then randomly sampled to generate a stochastic process Y from the replay buffer. We provide an analysis of the properties of the sampled process such as stationarity, Markovity and autocorrelation in terms of the properties of the original process. Our theoretical analysis sheds light on why replay buffer may be a good de-correlator. Our analysis provides theoretical tools for proving the convergence of replay buffer based algorithms which are prevalent in reinforcement learning schemes. | Shirli Di-Castro, Shie Mannor, Dotan Di Castro | null | null | 2,022 | icml |
Streaming Algorithms for High-Dimensional Robust Statistics | null | We study high-dimensional robust statistics tasks in the streaming model. A recent line of work obtained computationally efficient algorithms for a range of high-dimensional robust statistics tasks. Unfortunately, all previous algorithms require storing the entire dataset, incurring memory at least quadratic in the dimension. In this work, we develop the first efficient streaming algorithms for high-dimensional robust statistics with near-optimal memory requirements (up to logarithmic factors). Our main result is for the task of high-dimensional robust mean estimation in (a strengthening of) Huber’s contamination model. We give an efficient single-pass streaming algorithm for this task with near-optimal error guarantees and space complexity nearly-linear in the dimension. As a corollary, we obtain streaming algorithms with near-optimal space complexity for several more complex tasks, including robust covariance estimation, robust regression, and more generally robust stochastic optimization. | Ilias Diakonikolas, Daniel M. Kane, Ankit Pensia, Thanasis Pittas | null | null | 2,022 | icml |
On the Convergence of Inexact Predictor-Corrector Methods for Linear Programming | null | Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear system of equations at each iteration. In common applications of linear programming, particularly in machine learning and scientific computing, the size of this linear system can become prohibitively large, requiring the use of iterative solvers, which provide an approximate solution to the linear system. However, approximately solving the linear system at each iteration of an IPM invalidates the theoretical guarantees of common IPM analyses. To remedy this, we theoretically and empirically analyze (slightly modified) predictor-corrector IPMs when using approximate linear solvers: our approach guarantees that, when certain conditions are satisfied, the number of IPM iterations does not increase and that the final solution remains feasible. We also provide practical instantiations of approximate linear solvers that satisfy these conditions for special classes of constraint matrices using randomized linear algebra. | Gregory Dexter, Agniva Chowdhury, Haim Avron, Petros Drineas | null | null | 2,022 | icml |
Variational Feature Pyramid Networks | null | Recent architectures for object detection adopt a Feature Pyramid Network as a backbone for deep feature extraction. Many works focus on the design of pyramid networks which produce richer feature representations. In this work, we opt to learn a dataset-specific architecture for Feature Pyramid Networks. With the proposed method, the network fuses features at multiple scales, it is efficient in terms of parameters and operations, and yields better results across a variety of tasks and datasets. Starting by a complex network, we adopt Variational Inference to prune redundant connections. Our model, integrated with standard detectors, outperforms the state-of-the-art feature fusion networks. | Panagiotis Dimitrakopoulos, Giorgos Sfikas, Christophoros Nikou | null | null | 2,022 | icml |
Error-driven Input Modulation: Solving the Credit Assignment Problem without a Backward Pass | null | Supervised learning in artificial neural networks typically relies on backpropagation, where the weights are updated based on the error-function gradients and sequentially propagated from the output layer to the input layer. Although this approach has proven effective in a wide domain of applications, it lacks biological plausibility in many regards, including the weight symmetry problem, the dependence of learning on non-local signals, the freezing of neural activity during error propagation, and the update locking problem. Alternative training schemes have been introduced, including sign symmetry, feedback alignment, and direct feedback alignment, but they invariably rely on a backward pass that hinders the possibility of solving all the issues simultaneously. Here, we propose to replace the backward pass with a second forward pass in which the input signal is modulated based on the error of the network. We show that this novel learning rule comprehensively addresses all the above-mentioned issues and can be applied to both fully connected and convolutional models. We test this learning rule on MNIST, CIFAR-10, and CIFAR-100. These results help incorporate biological principles into machine learning. | Giorgia Dellaferrera, Gabriel Kreiman | null | null | 2,022 | icml |
Learning General Halfspaces with Adversarial Label Noise via Online Gradient Descent | null | We study the problem of learning general {—} i.e., not necessarily homogeneous {—} halfspaces with adversarial label noise under the Gaussian distribution. Prior work has provided a sophisticated polynomial-time algorithm for this problem. In this work, we show that the problem can be solved directly via online gradient descent applied to a sequence of natural non-convex surrogates. This approach yields a simple iterative learning algorithm for general halfspaces with near-optimal sample complexity, runtime, and error guarantee. At the conceptual level, our work establishes an intriguing connection between learning halfspaces with adversarial noise and online optimization that may find other applications. | Ilias Diakonikolas, Vasilis Kontonis, Christos Tzamos, Nikos Zarifis | null | null | 2,022 | icml |
Independent Policy Gradient for Large-Scale Markov Potential Games: Sharper Rates, Function Approximation, and Game-Agnostic Convergence | null | We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPGs). To learn a Nash equilibrium of an MPG in which the size of state space and/or the number of players can be very large, we propose new independent policy gradient algorithms that are run by all players in tandem. When there is no uncertainty in the gradient evaluation, we show that our algorithm finds an $\epsilon$-Nash equilibrium with $O(1/\epsilon^2)$ iteration complexity which does not explicitly depend on the state space size. When the exact gradient is not available, we establish $O(1/\epsilon^5)$ sample complexity bound in a potentially infinitely large state space for a sample-based algorithm that utilizes function approximation. Moreover, we identify a class of independent policy gradient algorithms that enjoy convergence for both zero-sum Markov games and Markov cooperative games with the players that are oblivious to the types of games being played. Finally, we provide computational experiments to corroborate the merits and the effectiveness of our theoretical developments. | Dongsheng Ding, Chen-Yu Wei, Kaiqing Zhang, Mihailo Jovanovic | null | null | 2,022 | icml |
Fair Generalized Linear Models with a Convex Penalty | null | Despite recent advances in algorithmic fairness, methodologies for achieving fairness with generalized linear models (GLMs) have yet to be explored in general, despite GLMs being widely used in practice. In this paper we introduce two fairness criteria for GLMs based on equalizing expected outcomes or log-likelihoods. We prove that for GLMs both criteria can be achieved via a convex penalty term based solely on the linear components of the GLM, thus permitting efficient optimization. We also derive theoretical properties for the resulting fair GLM estimator. To empirically demonstrate the efficacy of the proposed fair GLM, we compare it with other well-known fair prediction methods on an extensive set of benchmark datasets for binary classification and regression. In addition, we demonstrate that the fair GLM can generate fair predictions for a range of response variables, other than binary and continuous outcomes. | Hyungrok Do, Preston Putzel, Axel S Martin, Padhraic Smyth, Judy Zhong | null | null | 2,022 | icml |
PACE: A Parallelizable Computation Encoder for Directed Acyclic Graphs | null | Optimization of directed acyclic graph (DAG) structures has many applications, such as neural architecture search (NAS) and probabilistic graphical model learning. Encoding DAGs into real vectors is a dominant component in most neural-network-based DAG optimization frameworks. Currently, most popular DAG encoders use an asynchronous message passing scheme which sequentially processes nodes according to the dependency between nodes in a DAG. That is, a node must not be processed until all its predecessors are processed. As a result, they are inherently not parallelizable. In this work, we propose a Parallelizable Attention-based Computation structure Encoder (PACE) that processes nodes simultaneously and encodes DAGs in parallel. We demonstrate the superiority of PACE through encoder-dependent optimization subroutines that search the optimal DAG structure based on the learned DAG embeddings. Experiments show that PACE not only improves the effectiveness over previous sequential DAG encoders with a significantly boosted training and inference speed, but also generates smooth latent (DAG encoding) spaces that are beneficial to downstream optimization subroutines. | Zehao Dong, Muhan Zhang, Fuhai Li, Yixin Chen | null | null | 2,022 | icml |
Finding the Task-Optimal Low-Bit Sub-Distribution in Deep Neural Networks | null | Quantized neural networks typically require smaller memory footprints and lower computation complexity, which is crucial for efficient deployment. However, quantization inevitably leads to a distribution divergence from the original network, which generally degrades the performance. To tackle this issue, massive efforts have been made, but most existing approaches lack statistical considerations and depend on several manual configurations. In this paper, we present an adaptive-mapping quantization method to learn an optimal latent sub-distribution that is inherent within models and smoothly approximated with a concrete Gaussian Mixture (GM). In particular, the network weights are projected in compliance with the GM-approximated sub-distribution. This sub-distribution evolves along with the weight update in a co-tuning schema guided by the direct task-objective optimization. Sufficient experiments on image classification and object detection over various modern architectures demonstrate the effectiveness, generalization property, and transferability of the proposed method. Besides, an efficient deployment flow for the mobile CPU is developed, achieving up to 7.46$\times$ inference acceleration on an octa-core ARM CPU. Our codes have been publicly released at https://github.com/RunpeiDong/DGMS. | Runpei Dong, Zhanhong Tan, Mengdi Wu, Linfeng Zhang, Kaisheng Ma | null | null | 2,022 | icml |
Branching Reinforcement Learning | null | In this paper, we propose a novel Branching Reinforcement Learning (Branching RL) model, and investigate both Regret Minimization (RM) and Reward-Free Exploration (RFE) metrics for this model. Unlike standard RL where the trajectory of each episode is a single $H$-step path, branching RL allows an agent to take multiple base actions in a state such that transitions branch out to multiple successor states correspondingly, and thus it generates a tree-structured trajectory. This model finds important applications in hierarchical recommendation systems and online advertising. For branching RL, we establish new Bellman equations and key lemmas, i.e., branching value difference lemma and branching law of total variance, and also bound the total variance by only $O(H^2)$ under an exponentially-large trajectory. For RM and RFE metrics, we propose computationally efficient algorithms BranchVI and BranchRFE, respectively, and derive nearly matching upper and lower bounds. Our regret and sample complexity results are polynomial in all problem parameters despite exponentially-large trajectories. | Yihan Du, Wei Chen | null | null | 2,022 | icml |
TACTiS: Transformer-Attentional Copulas for Time Series | null | The estimation of time-varying quantities is a fundamental component of decision making in fields such as healthcare and finance. However, the practical utility of such estimates is limited by how accurately they quantify predictive uncertainty. In this work, we address the problem of estimating the joint predictive distribution of high-dimensional multivariate time series. We propose a versatile method, based on the transformer architecture, that estimates joint distributions using an attention-based decoder that provably learns to mimic the properties of non-parametric copulas. The resulting model has several desirable properties: it can scale to hundreds of time series, supports both forecasting and interpolation, can handle unaligned and non-uniformly sampled data, and can seamlessly adapt to missing data during training. We demonstrate these properties empirically and show that our model produces state-of-the-art predictions on multiple real-world datasets. | Alexandre Drouin, Étienne Marcotte, Nicolas Chapados | null | null | 2,022 | icml |
On the Difficulty of Defending Self-Supervised Learning against Model Extraction | null | Self-Supervised Learning (SSL) is an increasingly popular ML paradigm that trains models to transform complex inputs into representations without relying on explicit labels. These representations encode similarity structures that enable efficient learning of multiple downstream tasks. Recently, ML-as-a-Service providers have commenced offering trained SSL models over inference APIs, which transform user inputs into useful representations for a fee. However, the high cost involved to train these models and their exposure over APIs both make black-box extraction a realistic security threat. We thus explore model stealing attacks against SSL. Unlike traditional model extraction on classifiers that output labels, the victim models here output representations; these representations are of significantly higher dimensionality compared to the low-dimensional prediction scores output by classifiers. We construct several novel attacks and find that approaches that train directly on a victim’s stolen representations are query efficient and enable high accuracy for downstream models. We then show that existing defenses against model extraction are inadequate and not easily retrofitted to the specificities of SSL. | Adam Dziedzic, Nikita Dhawan, Muhammad Ahmad Kaleem, Jonas Guan, Nicolas Papernot | null | null | 2,022 | icml |
Augment with Care: Contrastive Learning for Combinatorial Problems | null | Supervised learning can improve the design of state-of-the-art solvers for combinatorial problems, but labelling large numbers of combinatorial instances is often impractical due to exponential worst-case complexity. Inspired by the recent success of contrastive pre-training for images, we conduct a scientific study of the effect of augmentation design on contrastive pre-training for the Boolean satisfiability problem. While typical graph contrastive pre-training uses label-agnostic augmentations, our key insight is that many combinatorial problems have well-studied invariances, which allow for the design of label-preserving augmentations. We find that label-preserving augmentations are critical for the success of contrastive pre-training. We show that our representations are able to achieve comparable test accuracy to fully-supervised learning while using only 1% of the labels. We also demonstrate that our representations are more transferable to larger problems from unseen domains. Our code is available at https://github.com/h4duan/contrastive-sat. | Haonan Duan, Pashootan Vaezipoor, Max B Paulus, Yangjun Ruan, Chris Maddison | null | null | 2,022 | icml |
Adapting to Mixing Time in Stochastic Optimization with Markovian Data | null | We consider stochastic optimization problems where data is drawn from a Markov chain. Existing methods for this setting crucially rely on knowing the mixing time of the chain, which in real-world applications is usually unknown. We propose the first optimization method that does not require the knowledge of the mixing time, yet obtains the optimal asymptotic convergence rate when applied to convex problems. We further show that our approach can be extended to: (i) finding stationary points in non-convex optimization with Markovian data, and (ii) obtaining better dependence on the mixing time in temporal difference (TD) learning; in both cases, our method is completely oblivious to the mixing time. Our method relies on a novel combination of multi-level Monte Carlo (MLMC) gradient estimation together with an adaptive learning method. | Ron Dorfman, Kfir Yehuda Levy | null | null | 2,022 | icml |
From data to functa: Your data point is a function and you can treat it like one | null | It is common practice in deep learning to represent a measurement of the world on a discrete grid, e.g. a 2D grid of pixels. However, the underlying signal represented by these measurements is often continuous, e.g. the scene depicted in an image. A powerful continuous alternative is then to represent these measurements using an implicit neural representation, a neural function trained to output the appropriate measurement value for any input spatial location. In this paper, we take this idea to its next level: what would it take to perform deep learning on these functions instead, treating them as data? In this context we refer to the data as functa, and propose a framework for deep learning on functa. This view presents a number of challenges around efficient conversion from data to functa, compact representation of functa, and effectively solving downstream tasks on functa. We outline a recipe to overcome these challenges and apply it to a wide range of data modalities including images, 3D shapes, neural radiance fields (NeRF) and data on manifolds. We demonstrate that this approach has various compelling properties across data modalities, in particular on the canonical tasks of generative modeling, data imputation, novel view synthesis and classification. | Emilien Dupont, Hyunjik Kim, S. M. Ali Eslami, Danilo Jimenez Rezende, Dan Rosenbaum | null | null | 2,022 | icml |
Deletion Robust Submodular Maximization over Matroids | null | Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary of the dataset that contains a high value independent set even after an adversary deleted some elements. We present constant-factor approximation algorithms, whose space complexity depends on the rank $k$ of the matroid and the number $d$ of deleted elements. In the centralized setting we present a $(3.582+O(\varepsilon))$-approximation algorithm with summary size $O(k + \frac{d}{\eps^2}\log \frac{k}{\eps})$. In the streaming setting we provide a $(5.582+O(\varepsilon))$-approximation algorithm with summary size and memory $O(k + \frac{d}{\eps^2}\log \frac{k}{\eps})$. We complement our theoretical results with an in-depth experimental analysis showing the effectiveness of our algorithms on real-world datasets. | Paul Duetting, Federico Fusco, Silvio Lattanzi, Ashkan Norouzi-Fard, Morteza Zadimoghaddam | null | null | 2,022 | icml |
GLaM: Efficient Scaling of Language Models with Mixture-of-Experts | null | Scaling language models with more data, compute and parameters has driven significant progress in natural language processing. For example, thanks to scaling, GPT-3 was able to achieve strong results on in-context learning tasks. However, training these large dense models requires significant amounts of computing resources. In this paper, we propose and develop a family of language models named \glam (\textbf{G}eneralist \textbf{La}nguage \textbf{M}odel), which uses a sparsely activated mixture-of-experts architecture to scale the model capacity while also incurring substantially less training cost compared to dense variants. The largest \glam has 1.2 trillion parameters, which is approximately 7x larger than GPT-3. It consumes only 1/3 of the energy used to train GPT-3 and requires half of the computation flops for inference, while still achieving better overall fewshot performance across 29 NLP tasks. | Nan Du, Yanping Huang, Andrew M Dai, Simon Tong, Dmitry Lepikhin, Yuanzhong Xu, Maxim Krikun, Yanqi Zhou, Adams Wei Yu, Orhan Firat, Barret Zoph, Liam Fedus, Maarten P Bosma, Zongwei Zhou, Tao Wang, Emma Wang, Kellie Webster, Marie Pellat, Kevin Robinson, Kathleen Meier-Hellstern, Toju Duke, Lucas Dixon, Kun Zhang, Quoc Le, Yonghui Wu, Zhifeng Chen, Claire Cui | null | null | 2,022 | icml |
Parametric Visual Program Induction with Function Modularization | null | Generating programs to describe visual observations has gained much research attention recently. However, most of the existing approaches are based on non-parametric primitive functions, making them unable to handle complex visual scenes involving many attributes and details. In this paper, we propose the concept of parametric visual program induction. Learning to generate parametric programs for visual scenes is challenging due to the huge number of function variants and the complex function correlations. To solve these challenges, we propose the method of function modularization, capable of dealing with numerous function variants and complex correlations. Specifically, we model each parametric function as a multi-head self-contained neural module to cover different function variants. Moreover, to eliminate the complex correlations between functions, we propose the hierarchical heterogeneous Monto-Carlo tree search (H2MCTS) algorithm which can provide high-quality uncorrelated supervision during training, and serve as an efficient searching technique during testing. We demonstrate the superiority of the proposed method on three visual program induction datasets involving parametric primitive functions. Experimental results show that our proposed model is able to significantly outperform the state-of-the-art baseline methods in terms of generating accurate programs. | Xuguang Duan, Xin Wang, Ziwei Zhang, Wenwu Zhu | null | null | 2,022 | icml |
Fast rates for noisy interpolation require rethinking the effect of inductive bias | null | Good generalization performance on high-dimensional data crucially hinges on a simple structure of the ground truth and a corresponding strong inductive bias of the estimator. Even though this intuition is valid for regularized models, in this paper we caution against a strong inductive bias for interpolation in the presence of noise: While a stronger inductive bias encourages a simpler structure that is more aligned with the ground truth, it also increases the detrimental effect of noise. Specifically, for both linear regression and classification with a sparse ground truth, we prove that minimum $\ell_p$-norm and maximum $\ell_p$-margin interpolators achieve fast polynomial rates close to order $1/n$ for $p > 1$ compared to a logarithmic rate for $p = 1$. Finally, we provide preliminary experimental evidence that this trade-off may also play a crucial role in understanding non-linear interpolating models used in practice. | Konstantin Donhauser, Nicolò Ruggeri, Stefan Stojanovic, Fanny Yang | null | null | 2,022 | icml |
A Context-Integrated Transformer-Based Neural Network for Auction Design | null | One of the central problems in auction design is developing an incentive-compatible mechanism that maximizes the auctioneer’s expected revenue. While theoretical approaches have encountered bottlenecks in multi-item auctions, recently, there has been much progress on finding the optimal mechanism through deep learning. However, these works either focus on a fixed set of bidders and items, or restrict the auction to be symmetric. In this work, we overcome such limitations by factoring public contextual information of bidders and items into the auction learning framework. We propose $\mathtt{CITransNet}$, a context-integrated transformer-based neural network for optimal auction design, which maintains permutation-equivariance over bids and contexts while being able to find asymmetric solutions. We show by extensive experiments that $\mathtt{CITransNet}$ can recover the known optimal solutions in single-item settings, outperform strong baselines in multi-item auctions, and generalize well to cases other than those in training. | Zhijian Duan, Jingwu Tang, Yutong Yin, Zhe Feng, Xiang Yan, Manzil Zaheer, Xiaotie Deng | null | null | 2,022 | icml |
Privacy for Free: How does Dataset Condensation Help Privacy? | null | To prevent unintentional data leakage, research community has resorted to data generators that can produce differentially private data for model training. However, for the sake of the data privacy, existing solutions suffer from either expensive training cost or poor generalization performance. Therefore, we raise the question whether training efficiency and privacy can be achieved simultaneously. In this work, we for the first time identify that dataset condensation (DC) which is originally designed for improving training efficiency is also a better solution to replace the traditional data generators for private data generation, thus providing privacy for free. To demonstrate the privacy benefit of DC, we build a connection between DC and differential privacy, and theoretically prove on linear feature extractors (and then extended to non-linear feature extractors) that the existence of one sample has limited impact ($O(m/n)$) on the parameter distribution of networks trained on $m$ samples synthesized from $n (n \gg m)$ raw samples by DC. We also empirically validate the visual privacy and membership privacy of DC-synthesized data by launching both the loss-based and the state-of-the-art likelihood-based membership inference attacks. We envision this work as a milestone for data-efficient and privacy-preserving machine learning. | Tian Dong, Bo Zhao, Lingjuan Lyu | null | null | 2,022 | icml |
Bayesian Imitation Learning for End-to-End Mobile Manipulation | null | In this work we investigate and demonstrate benefits of a Bayesian approach to imitation learning from multiple sensor inputs, as applied to the task of opening office doors with a mobile manipulator. Augmenting policies with additional sensor inputs{—}such as RGB + depth cameras{—}is a straightforward approach to improving robot perception capabilities, especially for tasks that may favor different sensors in different situations. As we scale multi-sensor robotic learning to unstructured real-world settings (e.g. offices, homes) and more complex robot behaviors, we also increase reliance on simulators for cost, efficiency, and safety. Consequently, the sim-to-real gap across multiple sensor modalities also increases, making simulated validation more difficult. We show that using the Variational Information Bottleneck (Alemi et al., 2016) to regularize convolutional neural networks improves generalization to heldout domains and reduces the sim-to-real gap in a sensor-agnostic manner. As a side effect, the learned embeddings also provide useful estimates of model uncertainty for each sensor. We demonstrate that our method is able to help close the sim-to-real gap and successfully fuse RGB and depth modalities based on understanding of the situational uncertainty of each sensor. In a real-world office environment, we achieve 96% task success, improving upon the baseline by +16%. | Yuqing Du, Daniel Ho, Alex Alemi, Eric Jang, Mohi Khansari | null | null | 2,022 | icml |
Bayesian Deep Embedding Topic Meta-Learner | null | Existing deep topic models are effective in capturing the latent semantic structures in textual data but usually rely on a plethora of documents. This is less than satisfactory in practical applications when only a limited amount of data is available. In this paper, we propose a novel framework that efficiently solves the problem of topic modeling under the small data regime. Specifically, the framework involves two innovations: a bi-level generative model that aims to exploit the task information to guide the document generation, and a topic meta-learner that strives to learn a group of global topic embeddings so that fast adaptation to the task-specific topic embeddings can be achieved with a few examples. We apply the proposed framework to a hierarchical embedded topic model and achieve better performance than various baseline models on diverse experiments, including few-shot topic discovery and few-shot document classification. | Zhibin Duan, Yishi Xu, Jianqiao Sun, Bo Chen, Wenchao Chen, Chaojie Wang, Mingyuan Zhou | null | null | 2,022 | icml |
Efficient Low Rank Convex Bounds for Pairwise Discrete Graphical Models | null | In this paper, we extend a Burer-Monteiro style method to compute low rank Semi-Definite Programming (SDP) bounds for the MAP problem on discrete graphical models with an arbitrary number of states and arbitrary pairwise potentials. We consider both a penalized constraint approach and a dedicated Block Coordinate Descent (BCD) approach which avoids large penalty coefficients in the cost matrix. We show our algorithm is decreasing. Experiments show that the BCD approach compares favorably to the penalized approach and to usual linear bounds relying on convergent message passing approaches. | Valentin Durante, George Katsirelos, Thomas Schiex | null | null | 2,022 | icml |
LIMO: Latent Inceptionism for Targeted Molecule Generation | null | Generation of drug-like molecules with high binding affinity to target proteins remains a difficult and resource-intensive task in drug discovery. Existing approaches primarily employ reinforcement learning, Markov sampling, or deep generative models guided by Gaussian processes, which can be prohibitively slow when generating molecules with high binding affinity calculated by computationally-expensive physics-based methods. We present Latent Inceptionism on Molecules (LIMO), which significantly accelerates molecule generation with an inceptionism-like technique. LIMO employs a variational autoencoder-generated latent space and property prediction by two neural networks in sequence to enable faster gradient-based reverse-optimization of molecular properties. Comprehensive experiments show that LIMO performs competitively on benchmark tasks and markedly outperforms state-of-the-art techniques on the novel task of generating drug-like compounds with high binding affinity, reaching nanomolar range against two protein targets. We corroborate these docking-based results with more accurate molecular dynamics-based calculations of absolute binding free energy and show that one of our generated drug-like compounds has a predicted $K_D$ (a measure of binding affinity) of $6 \cdot 10^{-14}$ M against the human estrogen receptor, well beyond the affinities of typical early-stage drug candidates and most FDA-approved drugs to their respective targets. Code is available at https://github.com/Rose-STL-Lab/LIMO. | Peter Eckmann, Kunyang Sun, Bo Zhao, Mudong Feng, Michael Gilson, Rose Yu | null | null | 2,022 | icml |
Provable Reinforcement Learning with a Short-Term Memory | null | Real-world sequential decision making problems commonly involve partial observability, which requires the agent to maintain a memory of history in order to infer the latent states, plan and make good decisions. Coping with partial observability in general is extremely challenging, as a number of worst-case statistical and computational barriers are known in learning Partially Observable Markov Decision Processes (POMDPs). Motivated by the problem structure in several physical applications, as well as a commonly used technique known as "frame stacking", this paper proposes to study a new subclass of POMDPs, whose latent states can be decoded by the most recent history of a short length m. We establish a set of upper and lower bounds on the sample complexity for learning near-optimal policies for this class of problems in both tabular and rich-observation settings (where the number of observations is enormous). In particular, in the rich-observation setting, we develop new algorithms using a novel "moment matching" approach with a sample complexity that scales exponentially with the short length m rather than the problem horizon, and is independent of the number of observations. Our results show that a short-term memory suffices for reinforcement learning in these environments. | Yonathan Efroni, Chi Jin, Akshay Krishnamurthy, Sobhan Miryoosefi | null | null | 2,022 | icml |
pathGCN: Learning General Graph Spatial Operators from Paths | null | Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined spatial operator based on the graph Laplacian is often chosen, allowing only the point-wise operations to be learnt. However, learning a meaningful spatial operator is critical for developing more expressive GCNs for improved performance. In this paper we propose pathGCN, a novel approach to learn the spatial operator from random paths on the graph. We analyze the convergence of our method and its difference from existing GCNs. Furthermore, we discuss several options of combining our learnt spatial operator with point-wise convolutions. Our extensive experiments on numerous datasets suggest that by properly learning both the spatial and point-wise convolutions, phenomena like over-smoothing can be inherently avoided, and new state-of-the-art performance is achieved. | Moshe Eliasof, Eldad Haber, Eran Treister | null | null | 2,022 | icml |
Discrete Tree Flows via Tree-Structured Permutations | null | While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows. Most notably, discrete flow-based models cannot be straightforwardly optimized with conventional deep learning methods because gradients of discrete functions are undefined or zero. Previous works approximate pseudo-gradients of the discrete functions but do not solve the problem on a fundamental level. In addition to that, backpropagation can be computationally burdensome compared to alternative discrete algorithms such as decision tree algorithms. Our approach seeks to reduce computational burden and remove the need for pseudo-gradients by developing a discrete flow based on decision trees—building upon the success of efficient tree-based methods for classification and regression for discrete data. We first define a tree-structured permutation (TSP) that compactly encodes a permutation of discrete data where the inverse is easy to compute; thus, we can efficiently compute the density value and sample new data. We then propose a decision tree algorithm to build TSPs that learns the tree structure and permutations at each node via novel criteria. We empirically demonstrate the feasibility of our method on multiple datasets. | Mai Elkady, Jim Lim, David I. Inouye | null | null | 2,022 | icml |
Towards Scaling Difference Target Propagation by Learning Backprop Targets | null | The development of biologically-plausible learning algorithms is important for understanding learning in the brain, but most of them fail to scale-up to real-world tasks, limiting their potential as explanations for learning by real brains. As such, it is important to explore learning algorithms that come with strong theoretical guarantees and can match the performance of backpropagation (BP) on complex tasks. One such algorithm is Difference Target Propagation (DTP), a biologically-plausible learning algorithm whose close relation with Gauss-Newton (GN) optimization has been recently established. However, the conditions under which this connection rigorously holds preclude layer-wise training of the feedback pathway synaptic weights (which is more biologically plausible). Moreover, good alignment between DTP weight updates and loss gradients is only loosely guaranteed and under very specific conditions for the architecture being trained. In this paper, we propose a novel feedback weight training scheme that ensures both that DTP approximates BP and that layer-wise feedback weight training can be restored without sacrificing any theoretical guarantees. Our theory is corroborated by experimental results and we report the best performance ever achieved by DTP on CIFAR-10 and ImageNet 32x32. | Maxence M Ernoult, Fabrice Normandin, Abhinav Moudgil, Sean Spinney, Eugene Belilovsky, Irina Rish, Blake Richards, Yoshua Bengio | null | null | 2,022 | icml |
Learning Iterative Reasoning through Energy Minimization | null | Deep learning has excelled on complex pattern recognition tasks such as image classification and object recognition. However, it struggles with tasks requiring nontrivial reasoning, such as algorithmic computation. Humans are able to solve such tasks through iterative reasoning – spending more time to think about harder tasks. Most existing neural networks, however, exhibit a fixed computational budget controlled by the neural network architecture, preventing additional computational processing on harder tasks. In this work, we present a new framework for iterative reasoning with neural networks. We train a neural network to parameterize an energy landscape over all outputs, and implement each step of the iterative reasoning as an energy minimization step to find a minimal energy solution. By formulating reasoning as an energy minimization problem, for harder problems that lead to more complex energy landscapes, we may then adjust our underlying computational budget by running a more complex optimization procedure. We empirically illustrate that our iterative reasoning approach can solve more accurate and generalizable algorithmic reasoning tasks in both graph and continuous domains. Finally, we illustrate that our approach can recursively solve algorithmic problems requiring nested reasoning. | Yilun Du, Shuang Li, Joshua Tenenbaum, Igor Mordatch | null | null | 2,022 | icml |
FedNew: A Communication-Efficient and Privacy-Preserving Newton-Type Method for Federated Learning | null | Newton-type methods are popular in federated learning due to their fast convergence. Still, they suffer from two main issues, namely: low communication efficiency and low privacy due to the requirement of sending Hessian information from clients to parameter server (PS). In this work, we introduced a novel framework called FedNew in which there is no need to transmit Hessian information from clients to PS, hence resolving the bottleneck to improve communication efficiency. In addition, FedNew hides the gradient information and results in a privacy-preserving approach compared to the existing state-of-the-art. The core novel idea in FedNew is to introduce a two level framework, and alternate between updating the inverse Hessian-gradient product using only one alternating direction method of multipliers (ADMM) step and then performing the global model update using Newton’s method. Though only one ADMM pass is used to approximate the inverse Hessian-gradient product at each iteration, we develop a novel theoretical approach to show the converging behavior of FedNew for convex problems. Additionally, a significant reduction in communication overhead is achieved by utilizing stochastic quantization. Numerical results using real datasets show the superiority of FedNew compared to existing methods in terms of communication costs. | Anis Elgabli, Chaouki Ben Issaid, Amrit Singh Bedi, Ketan Rajawat, Mehdi Bennis, Vaneet Aggarwal | null | null | 2,022 | icml |
For Learning in Symmetric Teams, Local Optima are Global Nash Equilibria | null | Although it has been known since the 1970s that a globally optimal strategy profile in a common-payoff game is a Nash equilibrium, global optimality is a strict requirement that limits the result’s applicability. In this work, we show that any locally optimal symmetric strategy profile is also a (global) Nash equilibrium. Furthermore, we show that this result is robust to perturbations to the common payoff and to the local optimum. Applied to machine learning, our result provides a global guarantee for any gradient method that finds a local optimum in symmetric strategy space. While this result indicates stability to unilateral deviation, we nevertheless identify broad classes of games where mixed local optima are unstable under joint, asymmetric deviations. We analyze the prevalence of instability by running learning algorithms in a suite of symmetric games, and we conclude by discussing the applicability of our results to multi-agent RL, cooperative inverse RL, and decentralized POMDPs. | Scott Emmons, Caspar Oesterheld, Andrew Critch, Vincent Conitzer, Stuart Russell | null | null | 2,022 | icml |
DRIBO: Robust Deep Reinforcement Learning via Multi-View Information Bottleneck | null | Deep reinforcement learning (DRL) agents are often sensitive to visual changes that were unseen in their training environments. To address this problem, we leverage the sequential nature of RL to learn robust representations that encode only task-relevant information from observations based on the unsupervised multi-view setting. Specif- ically, we introduce a novel contrastive version of the Multi-View Information Bottleneck (MIB) objective for temporal data. We train RL agents from pixels with this auxiliary objective to learn robust representations that can compress away task-irrelevant information and are predictive of task-relevant dynamics. This approach enables us to train high-performance policies that are robust to visual distractions and can generalize well to unseen environments. We demonstrate that our approach can achieve SOTA performance on a di- verse set of visual control tasks in the DeepMind Control Suite when the background is replaced with natural videos. In addition, we show that our approach outperforms well-established base- lines for generalization to unseen environments on the Procgen benchmark. Our code is open- sourced and available at https://github. com/BU-DEPEND-Lab/DRIBO. | Jiameng Fan, Wenchao Li | null | null | 2,022 | icml |
Robust Counterfactual Explanations for Tree-Based Ensembles | null | Counterfactual explanations inform ways to achieve a desired outcome from a machine learning model. However, such explanations are not robust to certain real-world changes in the underlying model (e.g., retraining the model, changing hyperparameters, etc.), questioning their reliability in several applications, e.g., credit lending. In this work, we propose a novel strategy - that we call RobX - to generate robust counterfactuals for tree-based ensembles, e.g., XGBoost. Tree-based ensembles pose additional challenges in robust counterfactual generation, e.g., they have a non-smooth and non-differentiable objective function, and they can change a lot in the parameter space under retraining on very similar data. We first introduce a novel metric - that we call Counterfactual Stability - that attempts to quantify how robust a counterfactual is going to be to model changes under retraining, and comes with desirable theoretical properties. Our proposed strategy RobX works with any counterfactual generation method (base method) and searches for robust counterfactuals by iteratively refining the counterfactual generated by the base method using our metric Counterfactual Stability. We compare the performance of RobX with popular counterfactual generation methods (for tree-based ensembles) across benchmark datasets. The results demonstrate that our strategy generates counterfactuals that are significantly more robust (nearly 100% validity after actual model changes) and also realistic (in terms of local outlier factor) over existing state-of-the-art methods. | Sanghamitra Dutta, Jason Long, Saumitra Mishra, Cecilia Tilli, Daniele Magazzeni | null | null | 2,022 | icml |
Generalized Data Distribution Iteration | null | To obtain higher sample efficiency and superior final performance simultaneously has been one of the major challenges for deep reinforcement learning (DRL). Previous work could handle one of these challenges but typically failed to address them concurrently. In this paper, we try to tackle these two challenges simultaneously. To achieve this, we firstly decouple these challenges into two classic RL problems: data richness and exploration-exploitation trade-off. Then, we cast these two problems into the training data distribution optimization problem, namely to obtain desired training data within limited interactions, and address them concurrently via i) explicit modeling and control of the capacity and diversity of behavior policy and ii) more fine-grained and adaptive control of selective/sampling distribution of the behavior policy using a monotonic data distribution optimization. Finally, we integrate this process into Generalized Policy Iteration (GPI) and obtain a more general framework called Generalized Data Distribution Iteration (GDI). We use the GDI framework to introduce operator-based versions of well-known RL methods from DQN to Agent57. Theoretical guarantee of the superiority of GDI compared with GPI is concluded. We also demonstrate our state-of-the-art (SOTA) performance on Arcade Learning Environment (ALE), wherein our algorithm has achieved 9620.98% mean human normalized score (HNS), 1146.39% median HNS, and surpassed 22 human world records using only 200M training frames. Our performance is comparable to Agent57’s while we consume 500 times less data. We argue that there is still a long way to go before obtaining real superhuman agents in ALE. | Jiajun Fan, Changnan Xiao | null | null | 2,022 | icml |
Data Determines Distributional Robustness in Contrastive Language Image Pre-training (CLIP) | null | Contrastively trained language-image models such as CLIP, ALIGN, and BASIC have demonstrated unprecedented robustness to multiple challenging natural distribution shifts. Since these language-image models differ from previous training approaches in several ways, an important question is what causes the large robustness gains. We answer this question via a systematic experimental investigation. Concretely, we study five different possible causes for the robustness gains: (i) the training set size, (ii) the training distribution, (iii) language supervision at training time, (iv) language supervision at test time, and (v) the contrastive loss function. Our experiments show that the more diverse training distribution is the main cause for the robustness gains, with the other factors contributing little to no robustness. Beyond our experimental results, we also introduce ImageNet-Captions, a version of ImageNet with original text annotations from Flickr, to enable further controlled experiments of language-image training. | Alex Fang, Gabriel Ilharco, Mitchell Wortsman, Yuhao Wan, Vaishaal Shankar, Achal Dave, Ludwig Schmidt | null | null | 2,022 | icml |
Streaming Algorithm for Monotone k-Submodular Maximization with Cardinality Constraints | null | Maximizing a monotone k-submodular function subject to cardinality constraints is a general model for several applications ranging from influence maximization with multiple products to sensor placement with multiple sensor types and online ad allocation. Due to the large problem scale in many applications and the online nature of ad allocation, a need arises for algorithms that process elements in a streaming fashion and possibly make online decisions. In this work, we develop a new streaming algorithm for maximizing a monotone k-submodular function subject to a per-coordinate cardinality constraint attaining an approximation guarantee close to the state of the art guarantee in the offline setting. Though not typical for streaming algorithms, our streaming algorithm also readily applies to the online setting with free disposal. Our algorithm is combinatorial and enjoys fast running time and small number of function evaluations. Furthermore, its guarantee improves as the cardinality constraints get larger, which is especially suited for the large scale applications. For the special case of maximizing a submodular function with large budgets, our combinatorial algorithm matches the guarantee of the state-of-the-art continuous algorithm, which requires significantly more time and function evaluations. | Alina Ene, Huy Nguyen | null | null | 2,022 | icml |
An Equivalence Between Data Poisoning and Byzantine Gradient Attacks | null | To study the resilience of distributed learning, the “Byzantine" literature considers a strong threat model where workers can report arbitrary gradients to the parameter server. Whereas this model helped obtain several fundamental results, it has sometimes been considered unrealistic, when the workers are mostly trustworthy machines. In this paper, we show a surprising equivalence between this model and data poisoning, a threat considered much more realistic. More specifically, we prove that every gradient attack can be reduced to data poisoning, in any personalized federated learning system with PAC guarantees (which we show are both desirable and realistic). This equivalence makes it possible to obtain new impossibility results on the resilience of any “robust” learning algorithm to data poisoning in highly heterogeneous applications, as corollaries of existing impossibility theorems on Byzantine machine learning. Moreover, using our equivalence, we derive a practical attack that we show (theoretically and empirically) can be very effective against classical personalized federated learning models. | Sadegh Farhadkhani, Rachid Guerraoui, Lê Nguyên Hoang, Oscar Villemaud | null | null | 2,022 | icml |
Cascaded Gaps: Towards Logarithmic Regret for Risk-Sensitive Reinforcement Learning | null | In this paper, we study gap-dependent regret guarantees for risk-sensitive reinforcement learning based on the entropic risk measure. We propose a novel definition of sub-optimality gaps, which we call cascaded gaps, and we discuss their key components that adapt to underlying structures of the problem. Based on the cascaded gaps, we derive non-asymptotic and logarithmic regret bounds for two model-free algorithms under episodic Markov decision processes. We show that, in appropriate settings, these bounds feature exponential improvement over existing ones that are independent of gaps. We also prove gap-dependent lower bounds, which certify the near optimality of the upper bounds. | Yingjie Fei, Ruitu Xu | null | null | 2,022 | icml |
Training Discrete Deep Generative Models via Gapped Straight-Through Estimator | null | While deep generative models have succeeded in image processing, natural language processing, and reinforcement learning, training that involves discrete random variables remains challenging due to the high variance of its gradient estimation process. Monte Carlo is a common solution used in most variance reduction approaches. However, this involves time-consuming resampling and multiple function evaluations. We propose a Gapped Straight-Through (GST) estimator to reduce the variance without incurring resampling overhead. This estimator is inspired by the essential properties of Straight-Through Gumbel-Softmax. We determine these properties and show via an ablation study that they are essential. Experiments demonstrate that the proposed GST estimator enjoys better performance compared to strong baselines on two discrete deep generative modeling tasks, MNIST-VAE and ListOps. | Ting-Han Fan, Ta-Chung Chi, Alexander I. Rudnicky, Peter J Ramadge | null | null | 2,022 | icml |
Variational Sparse Coding with Learned Thresholding | null | Sparse coding strategies have been lauded for their parsimonious representations of data that leverage low dimensional structure. However, inference of these codes typically relies on an optimization procedure with poor computational scaling in high-dimensional problems. For example, sparse inference in the representations learned in the high-dimensional intermediary layers of deep neural networks (DNNs) requires an iterative minimization to be performed at each training step. As such, recent, quick methods in variational inference have been proposed to infer sparse codes by learning a distribution over the codes with a DNN. In this work, we propose a new approach to variational sparse coding that allows us to learn sparse distributions by thresholding samples, avoiding the use of problematic relaxations. We first evaluate and analyze our method by training a linear generator, showing that it has superior performance, statistical efficiency, and gradient estimation compared to other sparse distributions. We then compare to a standard variational autoencoder using a DNN generator on the CelebA dataset. | Kion Fallah, Christopher J Rozell | null | null | 2,022 | icml |
Byzantine Machine Learning Made Easy By Resilient Averaging of Momentums | null | Byzantine resilience emerged as a prominent topic within the distributed machine learning community. Essentially, the goal is to enhance distributed optimization algorithms, such as distributed SGD, in a way that guarantees convergence despite the presence of some misbehaving (a.k.a., Byzantine) workers. Although a myriad of techniques addressing the problem have been proposed, the field arguably rests on fragile foundations. These techniques are hard to prove correct and rely on assumptions that are (a) quite unrealistic, i.e., often violated in practice, and (b) heterogeneous, i.e., making it difficult to compare approaches. We present RESAM (RESilient Averaging of Momentums), a unified framework that makes it simple to establish optimal Byzantine resilience, relying only on standard machine learning assumptions. Our framework is mainly composed of two operators: resilient averaging at the server and distributed momentum at the workers. We prove a general theorem stating the convergence of distributed SGD under RESAM. Interestingly, demonstrating and comparing the convergence of many existing techniques become direct corollaries of our theorem, without resorting to stringent assumptions. We also present an empirical evaluation of the practical relevance of RESAM. | Sadegh Farhadkhani, Rachid Guerraoui, Nirupam Gupta, Rafael Pinot, John Stephan | null | null | 2,022 | icml |
A Resilient Distributed Boosting Algorithm | null | Given a learning task where the data is distributed among several parties, communication is one of the fundamental resources which the parties would like to minimize. We present a distributed boosting algorithm which is resilient to a limited amount of noise. Our algorithm is similar to classical boosting algorithms, although it is equipped with a new component, inspired by Impagliazzo’s hard-core lemma (Impagliazzo, 1995), adding a robustness quality to the algorithm. We also complement this result by showing that resilience to any asymptotically larger noise is not achievable by a communication-efficient algorithm. | Yuval Filmus, Idan Mehalel, Shay Moran | null | null | 2,022 | icml |
Head2Toe: Utilizing Intermediate Representations for Better Transfer Learning | null | Transfer-learning methods aim to improve performance in a data-scarce target domain using a model pretrained on a data-rich source domain. A cost-efficient strategy, linear probing, involves freezing the source model and training a new classification head for the target domain. This strategy is outperformed by a more costly but state-of-the-art method – fine-tuning all parameters of the source model to the target domain – possibly because fine-tuning allows the model to leverage useful information from intermediate layers which is otherwise discarded by the later previously trained layers. We explore the hypothesis that these intermediate layers might be directly exploited. We propose a method, Head-to-Toe probing (Head2Toe), that selects features from all layers of the source model to train a classification head for the target-domain. In evaluations on the Visual Task Adaptation Benchmark-1k, Head2Toe matches performance obtained with fine-tuning on average while reducing training and storage cost hundred folds or more, but critically, for out-of-distribution transfer, Head2Toe outperforms fine-tuning. Code used in our experiments can be found in supplementary materials. | Utku Evci, Vincent Dumoulin, Hugo Larochelle, Michael C Mozer | null | null | 2,022 | icml |
Bayesian Continuous-Time Tucker Decomposition | null | Tensor decomposition is a dominant framework for multiway data analysis and prediction. Although practical data often contains timestamps for the observed entries, existing tensor decomposition approaches overlook or under-use this valuable time information. They either drop the timestamps or bin them into crude steps and hence ignore the temporal dynamics within each step or use simple parametric time coefficients. To overcome these limitations, we propose Bayesian Continuous-Time Tucker Decomposition. We model the tensor-core of the classical Tucker decomposition as a time-varying function, and place a Gaussian process prior to flexibly estimate all kinds of temporal dynamics. In this way, our model maintains the interpretability while is flexible enough to capture various complex temporal relationships between the tensor nodes. For efficient and high-quality posterior inference, we use the stochastic differential equation (SDE) representation of temporal GPs to build an equivalent state-space prior, which avoids huge kernel matrix computation and sparse/low-rank approximations. We then use Kalman filtering, RTS smoothing, and conditional moment matching to develop a scalable message passing inference algorithm. We show the advantage of our method in simulation and several real-world applications. | Shikai Fang, Akil Narayan, Robert Kirby, Shandian Zhe | null | null | 2,022 | icml |
Investigating Generalization by Controlling Normalized Margin | null | Weight norm $\|w\|$ and margin $\gamma$ participate in learning theory via the normalized margin $\gamma/\|w\|$. Since standard neural net optimizers do not control normalized margin, it is hard to test whether this quantity causally relates to generalization. This paper designs a series of experimental studies that explicitly control normalized margin and thereby tackle two central questions. First: does normalized margin always have a causal effect on generalization? The paper finds that no—networks can be produced where normalized margin has seemingly no relationship with generalization, counter to the theory of Bartlett et al. (2017). Second: does normalized margin ever have a causal effect on generalization? The paper finds that yes—in a standard training setup, test performance closely tracks normalized margin. The paper suggests a Gaussian process model as a promising explanation for this behavior. | Alexander R Farhang, Jeremy D Bernstein, Kushal Tirumala, Yang Liu, Yisong Yue | null | null | 2,022 | icml |
Matching Structure for Dual Learning | null | Many natural language processing (NLP) tasks appear in dual forms, which are generally solved by dual learning technique that models the dualities between the coupled tasks. In this work, we propose to further enhance dual learning with structure matching that explicitly builds structural connections in between. Starting with the dual text$\leftrightarrow$text generation, we perform dually-syntactic structure co-echoing of the region of interest (RoI) between the task pair, together with a syntax cross-reconstruction at the decoding side. We next extend the idea to a text$\leftrightarrow$non-text setup, making alignment between the syntactic-semantic structure. Over 2*14 tasks covering 5 dual learning scenarios, the proposed structure matching method shows its significant effectiveness in enhancing existing dual learning. Our method can retrieve the key RoIs that are highly crucial to the task performance. Besides NLP tasks, it is also revealed that our approach has great potential in facilitating more non-text$\leftrightarrow$non-text scenarios. | Hao Fei, Shengqiong Wu, Yafeng Ren, Meishan Zhang | null | null | 2,022 | icml |
An Intriguing Property of Geophysics Inversion | null | Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity) from surface-based geophysical measurements (e.g., seismic, electric/magnetic (EM) data). The problems are governed by partial differential equations (PDEs) like the wave or Maxwell’s equations. Solving geophysical inversion problems is challenging due to the ill-posedness and high computational cost. To alleviate those issues, recent studies leverage deep neural networks to learn the inversion mappings from measurements to the property directly. In this paper, we show that such a mapping can be well modeled by a very shallow (but not wide) network with only five layers. This is achieved based on our new finding of an intriguing property: a near-linear relationship between the input and output, after applying integral transform in high dimensional space. In particular, when dealing with the inversion from seismic data to subsurface velocity governed by a wave equation, the integral results of velocity with Gaussian kernels are linearly correlated to the integral of seismic data with sine kernels. Furthermore, this property can be easily turned into a light-weight encoder-decoder network for inversion. The encoder contains the integration of seismic data and the linear transformation without need for fine-tuning. The decoder only consists of a single transformer block to reverse the integral of velocity. Experiments show that this interesting property holds for two geophysics inversion problems over four different datasets. Compared to much deeper InversionNet, our method achieves comparable accuracy, but consumes significantly fewer parameters | Yinan Feng, Yinpeng Chen, Shihang Feng, Peng Jin, Zicheng Liu, Youzuo Lin | null | null | 2,022 | icml |
Local Linear Convergence of Douglas-Rachford for Linear Programming: a Probabilistic Analysis | null | Douglas-Rachford splitting/ADMM (henceforth DRS) is a very popular algorithm for solving convex optimisation problems to low or moderate accuracy, and in particular for solving large-scale linear programs. Despite recent progress, obtaining highly accurate solutions to linear programs with DRS remains elusive. In this paper we analyze the local linear convergence rate $r$ of the DRS method for random linear programs, and give explicit and tight bounds on $r$. We show that $1-r^2$ is typically of the order of $m^{-1}(n-m)^{-1}$, where $n$ is the number of variables and $m$ is the number of constraints. This provides a quantitative explanation for the very slow convergence of DRS/ADMM on random LPs. The proof of our result relies on an established characterisation of the linear rate of convergence as the cosine of the Friedrichs angle between two subspaces associated to the problem. We also show that the cosecant of this angle can be interpreted as a condition number for the LP. The proof of our result relies on a characterization of the linear rate of convergence as the cosine of the Friedrichs angle between two subspaces associated to the problem. We also show that the cosecant of this angle can be interpreted as a condition number for the LP. | Oisin Faust, Hamza Fawzi | null | null | 2,022 | icml |
Principled Knowledge Extrapolation with GANs | null | Human can extrapolate well, generalize daily knowledge into unseen scenarios, raise and answer counterfactual questions. To imitate this ability via generative models, previous works have extensively studied explicitly encoding Structural Causal Models (SCMs) into architectures of generator networks. This methodology, however, limits the flexibility of the generator as they must be carefully crafted to follow the causal graph, and demands a ground truth SCM with strong ignorability assumption as prior, which is a nontrivial assumption in many real scenarios. Thus, many current causal GAN methods fail to generate high fidelity counterfactual results as they cannot easily leverage state-of-the-art generative models. In this paper, we propose to study counterfactual synthesis from a new perspective of knowledge extrapolation, where a given knowledge dimension of the data distribution is extrapolated, but the remaining knowledge is kept indistinguishable from the original distribution. We show that an adversarial game with a closed-form discriminator can be used to address the knowledge extrapolation problem, and a novel principal knowledge descent method can efficiently estimate the extrapolated distribution through the adversarial game. Our method enjoys both elegant theoretical guarantees and superior performance in many scenarios. | Ruili Feng, Jie Xiao, Kecheng Zheng, Deli Zhao, Jingren Zhou, Qibin Sun, Zheng-Jun Zha | null | null | 2,022 | icml |
Contrastive Mixture of Posteriors for Counterfactual Inference, Data Integration and Fairness | null | Learning meaningful representations of data that can address challenges such as batch effect correction and counterfactual inference is a central problem in many domains including computational biology. Adopting a Conditional VAE framework, we show that marginal independence between the representation and a condition variable plays a key role in both of these challenges. We propose the Contrastive Mixture of Posteriors (CoMP) method that uses a novel misalignment penalty defined in terms of mixtures of the variational posteriors to enforce this independence in latent space. We show that CoMP has attractive theoretical properties compared to previous approaches, and we prove counterfactual identifiability of CoMP under additional assumptions. We demonstrate state-of-the-art performance on a set of challenging tasks including aligning human tumour samples with cancer cell-lines, predicting transcriptome-level perturbation responses, and batch correction on single-cell RNA sequencing data. We also find parallels to fair representation learning and demonstrate that CoMP is competitive on a common task in the field. | Adam Foster, Arpi Vezer, Craig A. Glastonbury, Paidi Creed, Samer Abujudeh, Aaron Sim | null | null | 2,022 | icml |
Coordinated Double Machine Learning | null | Double machine learning is a statistical method for leveraging complex black-box models to construct approximately unbiased treatment effect estimates given observational data with high-dimensional covariates, under the assumption of a partially linear model. The idea is to first fit on a subset of the samples two non-linear predictive models, one for the continuous outcome of interest and one for the observed treatment, and then to estimate a linear coefficient for the treatment using the remaining samples through a simple orthogonalized regression. While this methodology is flexible and can accommodate arbitrary predictive models, typically trained independently of one another, this paper argues that a carefully coordinated learning algorithm for deep neural networks may reduce the estimation bias. The improved empirical performance of the proposed method is demonstrated through numerical experiments on both simulated and real data. | Nitai Fingerhut, Matteo Sesia, Yaniv Romano | null | null | 2,022 | icml |
Fast Population-Based Reinforcement Learning on a Single Machine | null | Training populations of agents has demonstrated great promise in Reinforcement Learning for stabilizing training, improving exploration and asymptotic performance, and generating a diverse set of solutions. However, population-based training is often not considered by practitioners as it is perceived to be either prohibitively slow (when implemented sequentially), or computationally expensive (if agents are trained in parallel on independent accelerators). In this work, we compare implementations and revisit previous studies to show that the judicious use of compilation and vectorization allows population-based training to be performed on a single machine with one accelerator with minimal overhead compared to training a single agent. We also show that, when provided with a few accelerators, our protocols extend to large population sizes for applications such as hyperparameter tuning. We hope that this work and the public release of our code will encourage practitioners to use population-based learning techniques more frequently for their research and applications. | Arthur Flajolet, Claire Bizon Monroc, Karim Beguir, Thomas Pierrot | null | null | 2,022 | icml |
Revisiting Some Common Practices in Cooperative Multi-Agent Reinforcement Learning | null | Many advances in cooperative multi-agent reinforcement learning (MARL) are based on two common design principles: value decomposition and parameter sharing. A typical MARL algorithm of this fashion decomposes a centralized Q-function into local Q-networks with parameters shared across agents. Such an algorithmic paradigm enables centralized training and decentralized execution (CTDE) and leads to efficient learning in practice. Despite all the advantages, we revisit these two principles and show that in certain scenarios, e.g., environments with a highly multi-modal reward landscape, value decomposition, and parameter sharing can be problematic and lead to undesired outcomes. In contrast, policy gradient (PG) methods with individual policies provably converge to an optimal solution in these cases, which partially supports some recent empirical observations that PG can be effective in many MARL testbeds. Inspired by our theoretical analysis, we present practical suggestions on implementing multi-agent PG algorithms for either high rewards or diverse emergent behaviors and empirically validate our findings on a variety of domains, ranging from the simplified matrix and grid-world games to complex benchmarks such as StarCraft Multi-Agent Challenge and Google Research Football. We hope our insights could benefit the community towards developing more general and more powerful MARL algorithms. | Wei Fu, Chao Yu, Zelai Xu, Jiaqi Yang, Yi Wu | null | null | 2,022 | icml |
Kernelized Multiplicative Weights for 0/1-Polyhedral Games: Bridging the Gap Between Learning in Extensive-Form and Normal-Form Games | null | While extensive-form games (EFGs) can be converted into normal-form games (NFGs), doing so comes at the cost of an exponential blowup of the strategy space. So, progress on NFGs and EFGs has historically followed separate tracks, with the EFG community often having to catch up with advances (\eg last-iterate convergence and predictive regret bounds) from the larger NFG community. In this paper we show that the Optimistic Multiplicative Weights Update (OMWU) algorithm—the premier learning algorithm for NFGs—can be simulated on the normal-form equivalent of an EFG in linear time per iteration in the game tree size using a kernel trick. The resulting algorithm, Kernelized OMWU (KOMWU), applies more broadly to all convex games whose strategy space is a polytope with 0/1 integral vertices, as long as the kernel can be evaluated efficiently. In the particular case of EFGs, KOMWU closes several standing gaps between NFG and EFG learning, by enabling direct, black-box transfer to EFGs of desirable properties of learning dynamics that were so far known to be achievable only in NFGs. Specifically, KOMWU gives the first algorithm that guarantees at the same time last-iterate convergence, lower dependence on the size of the game tree than all prior algorithms, and $\tilde{\bigOh}(1)$ regret when followed by all players. | Gabriele Farina, Chung-Wei Lee, Haipeng Luo, Christian Kroer | null | null | 2,022 | icml |
Fast Relative Entropy Coding with A* coding | null | Relative entropy coding (REC) algorithms encode a sample from a target distribution Q using a proposal distribution P, such that the expected codelength is O(KL[Q || P]). REC can be seamlessly integrated with existing learned compression models since, unlike entropy coding, it does not assume discrete Q or P, and does not require quantisation. However, general REC algorithms require an intractable $\Omega$(exp(KL[Q || P])) runtime. We introduce AS* and AD* coding, two REC algorithms based on A* sampling. We prove that, for continuous distributions over the reals, if the density ratio is unimodal, AS* has O(D$\infty$[Q || P]) expected runtime, where D$\infty$[Q || P] is the Renyi $\infty$-divergence. We provide experimental evidence that AD* also has O(D$\infty$[Q || P]) expected runtime. We prove that AS* and AD* achieve an expected codelength of O(KL[Q || P]). Further, we introduce DAD*, an approximate algorithm based on AD* which retains its favourable runtime and has bias similar to that of alternative methods. Focusing on VAEs, we propose the IsoKL VAE (IKVAE), which can be used with DAD* to further improve compression efficiency. We evaluate A* coding with (IK)VAEs on MNIST, showing that it can losslessly compress images near the theoretically optimal limit. | Gergely Flamich, Stratis Markou, Jose Miguel Hernandez-Lobato | null | null | 2,022 | icml |
Private frequency estimation via projective geometry | null | In this work, we propose a new algorithm ProjectiveGeometryResponse (PGR) for locally differentially private (LDP) frequency estimation. For universe size of k and with n users, our eps-LDP algorithm has communication cost ceil(log_2 k) and computation cost O(n + k\exp(eps) log k) for the server to approximately reconstruct the frequency histogram, while achieve optimal privacy-utility tradeoff. In many practical settings this is a significant improvement over the O (n+k^2) computation cost that is achieved by the recent PI-RAPPOR algorithm (Feldman and Talwar; 2021). Our empirical evaluation shows a speedup of over 50x over PI-RAPPOR while using approximately 75x less memory. In addition, the running time of our algorithm is comparable to that of HadamardResponse (Acharya, Sun, and Zhang; 2019) and RecursiveHadamardResponse (Chen, Kairouz, and Ozgur; 2020) which have significantly worse reconstruction error. The error of our algorithm essentially matches that of the communication- and time-inefficient but utility-optimal SubsetSelection (SS) algorithm (Ye and Barg; 2017). Our new algorithm is based on using Projective Planes over a finite field to define a small collection of sets that are close to being pairwise independent and a dynamic programming algorithm for approximate histogram reconstruction for the server. | Vitaly Feldman, Jelani Nelson, Huy Nguyen, Kunal Talwar | null | null | 2,022 | icml |
Bregman Neural Networks | null | We present a framework based on bilevel optimization for learning multilayer, deep data representations. On the one hand, the lower-level problem finds a representation by successively minimizing layer-wise objectives made of the sum of a prescribed regularizer as well as a fidelity term and some linear function both depending on the representation found at the previous layer. On the other hand, the upper-level problem optimizes over the linear functions to yield a linearly separable final representation. We show that, by choosing the fidelity term as the quadratic distance between two successive layer-wise representations, the bilevel problem reduces to the training of a feed-forward neural network. Instead, by elaborating on Bregman distances, we devise a novel neural network architecture additionally involving the inverse of the activation function reminiscent of the skip connection used in ResNets. Numerical experiments suggest that the proposed Bregman variant benefits from better learning properties and more robust prediction performance. | Jordan Frecon, Gilles Gasso, Massimiliano Pontil, Saverio Salzo | null | null | 2,022 | icml |
SPDY: Accurate Pruning with Speedup Guarantees | null | The recent focus on the efficiency of deep neural networks (DNNs) has led to significant work on model compression approaches, of which weight pruning is one of the most popular. At the same time, there is rapidly-growing computational support for efficiently executing the unstructured-sparse models obtained via pruning. Yet, most existing pruning methods minimize just the number of remaining weights, i.e. the size of the model, rather than optimizing for inference time. We address this gap by introducing SPDY, a new compression method which automatically determines layer-wise sparsity targets achieving a desired inference speedup on a given system, while minimizing accuracy loss. SPDY is the composition of two new techniques. The first is an efficient and general dynamic programming algorithm for solving constrained layer-wise compression problems, given a set of layer-wise error scores. The second technique is a local search procedure for automatically determining such scores in an accurate and robust manner. Experiments across popular vision and language models show that SPDY guarantees speedups while recovering higher accuracy relative to existing strategies, both for one-shot and gradual pruning scenarios, and is compatible with most existing pruning approaches. We also extend our approach to the recently-proposed task of pruning with very little data, where we achieve the best known accuracy recovery when pruning to the GPU-supported 2:4 sparsity pattern. | Elias Frantar, Dan Alistarh | null | null | 2,022 | icml |
Why Should I Trust You, Bellman? The Bellman Error is a Poor Replacement for Value Error | null | In this work, we study the use of the Bellman equation as a surrogate objective for value prediction accuracy. While the Bellman equation is uniquely solved by the true value function over all state-action pairs, we find that the Bellman error (the difference between both sides of the equation) is a poor proxy for the accuracy of the value function. In particular, we show that (1) due to cancellations from both sides of the Bellman equation, the magnitude of the Bellman error is only weakly related to the distance to the true value function, even when considering all state-action pairs, and (2) in the finite data regime, the Bellman equation can be satisfied exactly by infinitely many suboptimal solutions. This means that the Bellman error can be minimized without improving the accuracy of the value function. We demonstrate these phenomena through a series of propositions, illustrative toy examples, and empirical analysis in standard benchmark domains. | Scott Fujimoto, David Meger, Doina Precup, Ofir Nachum, Shixiang Shane Gu | null | null | 2,022 | icml |
Conformal Prediction Sets with Limited False Positives | null | We develop a new approach to multi-label conformal prediction in which we aim to output a precise set of promising prediction candidates with a bounded number of incorrect answers. Standard conformal prediction provides the ability to adapt to model uncertainty by constructing a calibrated candidate set in place of a single prediction, with guarantees that the set contains the correct answer with high probability. In order to obey this coverage property, however, conformal sets can become inundated with noisy candidates—which can render them unhelpful in practice. This is particularly relevant to practical applications where there is a limited budget, and the cost (monetary or otherwise) associated with false positives is non-negligible. We propose to trade coverage for a notion of precision by enforcing that the presence of incorrect candidates in the predicted conformal sets (i.e., the total number of false positives) is bounded according to a user-specified tolerance. Subject to this constraint, our algorithm then optimizes for a generalized notion of set coverage (i.e., the true positive rate) that allows for any number of true answers for a given query (including zero). We demonstrate the effectiveness of this approach across a number of classification tasks in natural language processing, computer vision, and computational chemistry. | Adam Fisch, Tal Schuster, Tommi Jaakkola, Dr.Regina Barzilay | null | null | 2,022 | icml |
Greedy when Sure and Conservative when Uncertain about the Opponents | null | We develop a new approach, named Greedy when Sure and Conservative when Uncertain (GSCU), to competing online against unknown and nonstationary opponents. GSCU improves in four aspects: 1) introduces a novel way of learning opponent policy embeddings offline; 2) trains offline a single best response (conditional additionally on our opponent policy embedding) instead of a finite set of separate best responses against any opponent; 3) computes online a posterior of the current opponent policy embedding, without making the discrete and ineffective decision which type the current opponent belongs to; and 4) selects online between a real-time greedy policy and a fixed conservative policy via an adversarial bandit algorithm, gaining a theoretically better regret than adhering to either. Experimental studies on popular benchmarks demonstrate GSCU’s superiority over the state-of-the-art methods. The code is available online at \url{https://github.com/YeTianJHU/GSCU}. | Haobo Fu, Ye Tian, Hongxiang Yu, Weiming Liu, Shuang Wu, Jiechao Xiong, Ying Wen, Kai Li, Junliang Xing, Qiang Fu, Wei Yang | null | null | 2,022 | icml |
The Complexity of k-Means Clustering when Little is Known | null | In the area of data analysis and arguably even in machine learning as a whole, few approaches have been as impactful as the classical k-means clustering. Here, we study the complexity of k-means clustering in settings where most of the data is not known or simply irrelevant. To obtain a more fine-grained understanding of the tractability of this clustering problem, we apply the parameterized complexity paradigm and obtain three new algorithms for k-means clustering of incomplete data: one for the clustering of bounded-domain (i.e., integer) data, and two incomparable algorithms that target real-valued data. Our approach is based on exploiting structural properties of a graphical encoding of the missing entries, and we show that tractability can be achieved using significantly less restrictive parameterizations than in the complementary case of few missing entries. | Robert Ganian, Thekla Hamm, Viktoriia Korchemna, Karolina Okrasa, Kirill Simonov | null | null | 2,022 | icml |
Extracting Latent State Representations with Linear Dynamics from Rich Observations | null | Recently, many reinforcement learning techniques have been shown to have provable guarantees in the simple case of linear dynamics, especially in problems like linear quadratic regulators. However, in practice many tasks require learning a policy from rich, high-dimensional features such as images, which are unlikely to be linear. We consider a setting where there is a hidden linear subspace of the high-dimensional feature space in which the dynamics are linear. We design natural objectives based on forward and inverse dynamics models. We prove that these objectives can be efficiently optimized and their local optimizers extract the hidden linear subspace. We empirically verify our theoretical results with synthetic data and explore the effectiveness of our approach (generalized to nonlinear settings) in simple control tasks with rich observations. | Abraham Frandsen, Rong Ge, Holden Lee | null | null | 2,022 | icml |
Robin Hood and Matthew Effects: Differential Privacy Has Disparate Impact on Synthetic Data | null | Generative models trained with Differential Privacy (DP) can be used to generate synthetic data while minimizing privacy risks. We analyze the impact of DP on these models vis-a-vis underrepresented classes/subgroups of data, specifically, studying: 1) the size of classes/subgroups in the synthetic data, and 2) the accuracy of classification tasks run on them. We also evaluate the effect of various levels of imbalance and privacy budgets. Our analysis uses three state-of-the-art DP models (PrivBayes, DP-WGAN, and PATE-GAN) and shows that DP yields opposite size distributions in the generated synthetic data. It affects the gap between the majority and minority classes/subgroups; in some cases by reducing it (a "Robin Hood" effect) and, in others, by increasing it (a "Matthew" effect). Either way, this leads to (similar) disparate impacts on the accuracy of classification tasks on the synthetic data, affecting disproportionately more the underrepresented subparts of the data. Consequently, when training models on synthetic data, one might incur the risk of treating different subpopulations unevenly, leading to unreliable or unfair conclusions. | Georgi Ganev, Bristena Oprisanu, Emiliano De Cristofaro | null | null | 2,022 | icml |
Loss Function Learning for Domain Generalization by Implicit Gradient | null | Generalising robustly to distribution shift is a major challenge that is pervasive across most real-world applications of machine learning. A recent study highlighted that many advanced algorithms proposed to tackle such domain generalisation (DG) fail to outperform a properly tuned empirical risk minimisation (ERM) baseline. We take a different approach, and explore the impact of the ERM loss function on out-of-domain generalisation. In particular, we introduce a novel meta-learning approach to loss function search based on implicit gradient. This enables us to discover a general purpose parametric loss function that provides a drop-in replacement for cross-entropy. Our loss can be used in standard training pipelines to efficiently train robust models using any neural architecture on new datasets. The results show that it clearly surpasses cross-entropy, enables simple ERM to outperform some more complicated prior DG methods, and provides state-of-the-art performance across a variety of DG benchmarks. Furthermore, unlike most existing DG approaches, our setup applies to the most practical setting of single-source domain generalisation, on which we show significant improvement. | Boyan Gao, Henry Gouk, Yongxin Yang, Timothy Hospedales | null | null | 2,022 | icml |
On the Convergence of Local Stochastic Compositional Gradient Descent with Momentum | null | Federated Learning has been actively studied due to its efficiency in numerous real-world applications in the past few years. However, the federated stochastic compositional optimization problem is still underexplored, even though it has widespread applications in machine learning. In this paper, we developed a novel local stochastic compositional gradient descent with momentum method, which facilitates Federated Learning for the stochastic compositional problem. Importantly, we investigated the convergence rate of our proposed method and proved that it can achieve the $O(1/\epsilon^4)$ sample complexity, which is better than existing methods. Meanwhile, our communication complexity $O(1/\epsilon^3)$ can match existing methods. To the best of our knowledge, this is the first work achieving such favorable sample and communication complexities. Additionally, extensive experimental results demonstrate the superior empirical performance over existing methods, confirming the efficacy of our method. | Hongchang Gao, Junyi Li, Heng Huang | null | null | 2,022 | icml |
On the Equivalence Between Temporal and Static Equivariant Graph Representations | null | This work formalizes the associational task of predicting node attribute evolution in temporal graphs from the perspective of learning equivariant representations. We show that node representations in temporal graphs can be cast into two distinct frameworks: (a) The most popular approach, which we denote as time-and-graph, where equivariant graph (e.g., GNN) and sequence (e.g., RNN) representations are intertwined to represent the temporal evolution of node attributes in the graph; and (b) an approach that we denote as time-then-graph, where the sequences describing the node and edge dynamics are represented first, then fed as node and edge attributes into a static equivariant graph representation that comes after. Interestingly, we show that time-then-graph representations have an expressivity advantage over time-and-graph representations when both use component GNNs that are not most-expressive (e.g., 1-Weisfeiler-Lehman GNNs). Moreover, while our goal is not necessarily to obtain state-of-the-art results, our experiments show that time-then-graph methods are capable of achieving better performance and efficiency than state-of-the-art time-and-graph methods in some real-world tasks, thereby showcasing that the time-then-graph framework is a worthy addition to the graph ML toolbox. | Jianfei Gao, Bruno Ribeiro | null | null | 2,022 | icml |
Generalizing Gaussian Smoothing for Random Search | null | Gaussian smoothing (GS) is a derivative-free optimization (DFO) algorithm that estimates the gradient of an objective using perturbations of the current parameters sampled from a standard normal distribution. We generalize it to sampling perturbations from a larger family of distributions. Based on an analysis of DFO for non-convex functions, we propose to choose a distribution for perturbations that minimizes the mean squared error (MSE) of the gradient estimate. We derive three such distributions with provably smaller MSE than Gaussian smoothing. We conduct evaluations of the three sampling distributions on linear regression, reinforcement learning, and DFO benchmarks in order to validate our claims. Our proposal improves on GS with the same computational complexity, and are competitive with and usually outperform Guided ES and Orthogonal ES, two computationally more expensive algorithms that adapt the covariance matrix of normally distributed perturbations. | Katelyn Gao, Ozan Sener | null | null | 2,022 | icml |
Lazy Estimation of Variable Importance for Large Neural Networks | null | As opaque predictive models increasingly impact many areas of modern life, interest in quantifying the importance of a given input variable for making a specific prediction has grown. Recently, there has been a proliferation of model-agnostic methods to measure variable importance (VI) that analyze the difference in predictive power between a full model trained on all variables and a reduced model that excludes the variable(s) of interest. A bottleneck common to these methods is the estimation of the reduced model for each variable (or subset of variables), which is an expensive process that often does not come with theoretical guarantees. In this work, we propose a fast and flexible method for approximating the reduced model with important inferential guarantees. We replace the need for fully retraining a wide neural network by a linearization initialized at the full model parameters. By adding a ridge-like penalty to make the problem convex, we prove that when the ridge penalty parameter is sufficiently large, our method estimates the variable importance measure with an error rate of O(1/n) where n is the number of training samples. We also show that our estimator is asymptotically normal, enabling us to provide confidence bounds for the VI estimates. We demonstrate through simulations that our method is fast and accurate under several data-generating regimes, and we demonstrate its real-world applicability on a seasonal climate forecasting example. | Yue Gao, Abby Stevens, Garvesh Raskutti, Rebecca Willett | null | null | 2,022 | icml |
Rethinking Image-Scaling Attacks: The Interplay Between Vulnerabilities in Machine Learning Systems | null | As real-world images come in varying sizes, the machine learning model is part of a larger system that includes an upstream image scaling algorithm. In this paper, we investigate the interplay between vulnerabilities of the image scaling procedure and machine learning models in the decision-based black-box setting. We propose a novel sampling strategy to make a black-box attack exploit vulnerabilities in scaling algorithms, scaling defenses, and the final machine learning model in an end-to-end manner. Based on this scaling-aware attack, we reveal that most existing scaling defenses are ineffective under threat from downstream models. Moreover, we empirically observe that standard black-box attacks can significantly improve their performance by exploiting the vulnerable scaling procedure. We further demonstrate this problem on a commercial Image Analysis API with decision-based black-box attacks. | Yue Gao, Ilia Shumailov, Kassem Fawaz | null | null | 2,022 | icml |
DepthShrinker: A New Compression Paradigm Towards Boosting Real-Hardware Efficiency of Compact Neural Networks | null | Efficient deep neural network (DNN) models equipped with compact operators (e.g., depthwise convolutions) have shown great potential in reducing DNNs’ theoretical complexity (e.g., the total number of weights/operations) while maintaining a decent model accuracy. However, existing efficient DNNs are still limited in fulfilling their promise in boosting real-hardware efficiency, due to their commonly adopted compact operators’ low hardware utilization. In this work, we open up a new compression paradigm for developing real-hardware efficient DNNs, leading to boosted hardware efficiency while maintaining model accuracy. Interestingly, we observe that while some DNN layers’ activation functions help DNNs’ training optimization and achievable accuracy, they can be properly removed after training without compromising the model accuracy. Inspired by this observation, we propose a framework dubbed DepthShrinker, which develops hardware-friendly compact networks via shrinking the basic building blocks of existing efficient DNNs that feature irregular computation patterns into dense ones with much improved hardware utilization and thus real-hardware efficiency. Excitingly, our DepthShrinker framework delivers hardware-friendly compact networks that outperform both state-of-the-art efficient DNNs and compression techniques, e.g., a 3.06% higher accuracy and 1.53x throughput on Tesla V100 over SOTA channel-wise pruning method MetaPruning. Our codes are available at: https://github.com/facebookresearch/DepthShrinker. | Yonggan Fu, Haichuan Yang, Jiayi Yuan, Meng Li, Cheng Wan, Raghuraman Krishnamoorthi, Vikas Chandra, Yingyan Lin | null | null | 2,022 | icml |
The power of first-order smooth optimization for black-box non-smooth problems | null | Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration complexity, and propose a generic approach that, based on optimal first-order methods, allows to obtain in a black-box fashion new zeroth-order algorithms for non-smooth convex optimization problems. Our approach not only leads to optimal oracle complexity, but also allows to obtain iteration complexity similar to first-order methods, which, in turn, allows to exploit parallel computations to accelerate the convergence of our algorithms. We also elaborate on extensions for stochastic optimization problems, saddle-point problems, and distributed optimization. | Alexander Gasnikov, Anton Novitskii, Vasilii Novitskii, Farshed Abdukhakimov, Dmitry Kamzolov, Aleksandr Beznosikov, Martin Takac, Pavel Dvurechensky, Bin Gu | null | null | 2,022 | icml |
PAGE-PG: A Simple and Loopless Variance-Reduced Policy Gradient Method with Probabilistic Gradient Estimation | null | Despite their success, policy gradient methods suffer from high variance of the gradient estimator, which can result in unsatisfactory sample complexity. Recently, numerous variance-reduced extensions of policy gradient methods with provably better sample complexity and competitive numerical performance have been proposed. After a compact survey on some of the main variance-reduced REINFORCE-type methods, we propose ProbAbilistic Gradient Estimation for Policy Gradient (PAGE-PG), a novel loopless variance-reduced policy gradient method based on a probabilistic switch between two types of update. Our method is inspired by the PAGE estimator for supervised learning and leverages importance sampling to obtain an unbiased gradient estimator. We show that PAGE-PG enjoys a $\mathcal{O}\left( \epsilon^{-3} \right)$ average sample complexity to reach an $\epsilon$-stationary solution, which matches the sample complexity of its most competitive counterparts under the same setting. A numerical evaluation confirms the competitive performance of our method on classical control tasks. | Matilde Gargiani, Andrea Zanelli, Andrea Martinelli, Tyler Summers, John Lygeros | null | null | 2,022 | icml |
Fast and Reliable Evaluation of Adversarial Robustness with Minimum-Margin Attack | null | The AutoAttack (AA) has been the most reliable method to evaluate adversarial robustness when considerable computational resources are available. However, the high computational cost (e.g., 100 times more than that of the project gradient descent attack) makes AA infeasible for practitioners with limited computational resources, and also hinders applications of AA in the adversarial training (AT). In this paper, we propose a novel method, minimum-margin (MM) attack, to fast and reliably evaluate adversarial robustness. Compared with AA, our method achieves comparable performance but only costs 3% of the computational time in extensive experiments. The reliability of our method lies in that we evaluate the quality of adversarial examples using the margin between two targets that can precisely identify the most adversarial example. The computational efficiency of our method lies in an effective Sequential TArget Ranking Selection (STARS) method, ensuring that the cost of the MM attack is independent of the number of classes. The MM attack opens a new way for evaluating adversarial robustness and provides a feasible and reliable way to generate high-quality adversarial examples in AT. | Ruize Gao, Jiongxiao Wang, Kaiwen Zhou, Feng Liu, Binghui Xie, Gang Niu, Bo Han, James Cheng | null | null | 2,022 | icml |
IDYNO: Learning Nonparametric DAGs from Interventional Dynamic Data | null | Causal discovery in the form of a directed acyclic graph (DAG) for time series data has been widely studied in various domains. The resulting DAG typically represents a dynamic Bayesian network (DBN), capturing both the instantaneous and time-delayed relationships among variables of interest. We propose a new algorithm, IDYNO, to learn the DAG structure from potentially nonlinear times series data by using a continuous optimization framework that includes a recent formulation for continuous acyclicity constraint. The proposed algorithm is designed to handle both observational and interventional time series data. We demonstrate the promising performance of our method on synthetic benchmark datasets against state-of-the-art baselines. In addition, we show that the proposed method can more accurately learn the underlying structure of a sequential decision model, such as a Markov decision process, with a fixed policy in typical continuous control tasks. | Tian Gao, Debarun Bhattacharjya, Elliot Nelson, Miao Liu, Yue Yu | null | null | 2,022 | icml |
Deep Reference Priors: What is the best way to pretrain a model? | null | What is the best way to exploit extra data – be it unlabeled data from the same task, or labeled data from a related task – to learn a given task? This paper formalizes the question using the theory of reference priors. Reference priors are objective, uninformative Bayesian priors that maximize the mutual information between the task and the weights of the model. Such priors enable the task to maximally affect the Bayesian posterior, e.g., reference priors depend upon the number of samples available for learning the task and for very small sample sizes, the prior puts more probability mass on low-complexity models in the hypothesis space. This paper presents the first demonstration of reference priors for medium-scale deep networks and image-based data. We develop generalizations of reference priors and demonstrate applications to two problems. First, by using unlabeled data to compute the reference prior, we develop new Bayesian semi-supervised learning methods that remain effective even with very few samples per class. Second, by using labeled data from the source task to compute the reference prior, we develop a new pretraining method for transfer learning that allows data from the target task to maximally affect the Bayesian posterior. Empirical validation of these methods is conducted on image classification datasets. Code is available at https://github.com/grasp-lyrl/deep_reference_priors | Yansong Gao, Rahul Ramesh, Pratik Chaudhari | null | null | 2,022 | icml |
(Non-)Convergence Results for Predictive Coding Networks | null | Predictive coding networks (PCNs) are (un)supervised learning models, coming from neuroscience, that approximate how the brain works. One major open problem around PCNs is their convergence behavior. In this paper, we use dynamical systems theory to formally investigate the convergence of PCNs as they are used in machine learning. Doing so, we put their theory on a firm, rigorous basis, by developing a precise mathematical framework for PCN and show that for sufficiently small weights and initializations, PCNs converge for any input. Thereby, we provide the theoretical assurance that previous implementations, whose convergence was assessed solely by numerical experiments, can indeed capture the correct behavior of PCNs. Outside of the identified regime of small weights and small initializations, we show via a counterexample that PCNs can diverge, countering common beliefs held in the community. This is achieved by identifying a Neimark-Sacker bifurcation in a PCN of small size, which gives rise to an unstable fixed point and an invariant curve around it. | Simon Frieder, Thomas Lukasiewicz | null | null | 2,022 | icml |
Stochastic smoothing of the top-K calibrated hinge loss for deep imbalanced classification | null | In modern classification tasks, the number of labels is getting larger and larger, as is the size of the datasets encountered in practice. As the number of classes increases, class ambiguity and class imbalance become more and more problematic to achieve high top-1 accuracy. Meanwhile, Top-K metrics (metrics allowing K guesses) have become popular, especially for performance reporting. Yet, proposing top-K losses tailored for deep learning remains a challenge, both theoretically and practically. In this paper we introduce a stochastic top-K hinge loss inspired by recent developments on top-K calibrated losses. Our proposal is based on the smoothing of the top-K operator building on the flexible "perturbed optimizer" framework. We show that our loss function performs very well in the case of balanced datasets, while benefiting from a significantly lower computational time than the state-of-the-art top-K loss function. In addition, we propose a simple variant of our loss for the imbalanced case. Experiments on a heavy-tailed dataset show that our loss function significantly outperforms other baseline loss functions. | Camille Garcin, Maximilien Servajean, Alexis Joly, Joseph Salmon | null | null | 2,022 | icml |
A Functional Information Perspective on Model Interpretation | null | Contemporary predictive models are hard to interpret as their deep nets exploit numerous complex relations between input elements. This work suggests a theoretical framework for model interpretability by measuring the contribution of relevant features to the functional entropy of the network with respect to the input. We rely on the log-Sobolev inequality that bounds the functional entropy by the functional Fisher information with respect to the covariance of the data. This provides a principled way to measure the amount of information contribution of a subset of features to the decision function. Through extensive experiments, we show that our method surpasses existing interpretability sampling-based methods on various data signals such as image, text, and audio. | Itai Gat, Nitay Calderon, Roi Reichart, Tamir Hazan | null | null | 2,022 | icml |
Near-Exact Recovery for Tomographic Inverse Problems via Deep Learning | null | This work is concerned with the following fundamental question in scientific machine learning: Can deep-learning-based methods solve noise-free inverse problems to near-perfect accuracy? Positive evidence is provided for the first time, focusing on a prototypical computed tomography (CT) setup. We demonstrate that an iterative end-to-end network scheme enables reconstructions close to numerical precision, comparable to classical compressed sensing strategies. Our results build on our winning submission to the recent AAPM DL-Sparse-View CT Challenge. Its goal was to identify the state-of-the-art in solving the sparse-view CT inverse problem with data-driven techniques. A specific difficulty of the challenge setup was that the precise forward model remained unknown to the participants. Therefore, a key feature of our approach was to initially estimate the unknown fanbeam geometry in a data-driven calibration step. Apart from an in-depth analysis of our methodology, we also demonstrate its state-of-the-art performance on the open-access real-world dataset LoDoPaB CT. | Martin Genzel, Ingo Gühring, Jan Macdonald, Maximilian März | null | null | 2,022 | icml |
A Regret Minimization Approach to Multi-Agent Control | null | We study the problem of multi-agent control of a dynamical system with known dynamics and adversarial disturbances. Our study focuses on optimal control without centralized precomputed policies, but rather with adaptive control policies for the different agents that are only equipped with a stabilizing controller. We give a reduction from any (standard) regret minimizing control method to a distributed algorithm. The reduction guarantees that the resulting distributed algorithm has low regret relative to the optimal precomputed joint policy. Our methodology involves generalizing online convex optimization to a multi-agent setting and applying recent tools from nonstochastic control derived for a single agent. We empirically evaluate our method on a model of an overactuated aircraft. We show that the distributed method is robust to failure and to adversarial perturbations in the dynamics. | Udaya Ghai, Udari Madhushani, Naomi Leonard, Elad Hazan | null | null | 2,022 | icml |
UniRank: Unimodal Bandit Algorithms for Online Ranking | null | We tackle, in the multiple-play bandit setting, the online ranking problem of assigning L items to K predefined positions on a web page in order to maximize the number of user clicks. We propose a generic algorithm, UniRank, that tackles state-of-the-art click models. The regret bound of this algorithm is a direct consequence of the pseudo-unimodality property of the bandit setting with respect to a graph where nodes are ordered sets of indistinguishable items. The main contribution of UniRank is its O(L/$\Delta$ logT) regret for T consecutive assignments, where $\Delta$ relates to the reward-gap between two items. This regret bound is based on the usually implicit condition that two items may not have the same attractiveness. Experiments against state-of-the-art learning algorithms specialized or not for different click models, show that our method has better regret performance than other generic algorithms on real life and synthetic datasets. | Camille-Sovanneary Gauthier, Romaric Gaudel, Elisa Fromont | null | null | 2,022 | icml |
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