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Randomized Exploration in Reinforcement Learning with General Value Function Approximation | null | We propose a model-free reinforcement learning algorithm inspired by the popular randomized least squares value iteration (RLSVI) algorithm as well as the optimism principle. Unlike existing upper-confidence-bound (UCB) based approaches, which are often computationally intractable, our algorithm drives exploration by simply perturbing the training data with judiciously chosen i.i.d. scalar noises. To attain optimistic value function estimation without resorting to a UCB-style bonus, we introduce an optimistic reward sampling procedure. When the value functions can be represented by a function class $\mathcal{F}$, our algorithm achieves a worst-case regret bound of $\tilde{O}(\mathrm{poly}(d_EH)\sqrt{T})$ where $T$ is the time elapsed, $H$ is the planning horizon and $d_E$ is the \emph{eluder dimension} of $\mathcal{F}$. In the linear setting, our algorithm reduces to LSVI-PHE, a variant of RLSVI, that enjoys an $\tilde{\mathcal{O}}(\sqrt{d^3H^3T})$ regret. We complement the theory with an empirical evaluation across known difficult exploration tasks. | Haque Ishfaq, Qiwen Cui, Viet Nguyen, Alex Ayoub, Zhuoran Yang, Zhaoran Wang, Doina Precup, Lin Yang | null | null | 2,021 | icml |
Fast margin maximization via dual acceleration | null | We present and analyze a momentum-based gradient method for training linear classifiers with an exponentially-tailed loss (e.g., the exponential or logistic loss), which maximizes the classification margin on separable data at a rate of O(1/t^2). This contrasts with a rate of O(1/log(t)) for standard gradient descent, and O(1/t) for normalized gradient descent. The momentum-based method is derived via the convex dual of the maximum-margin problem, and specifically by applying Nesterov acceleration to this dual, which manages to result in a simple and intuitive method in the primal. This dual view can also be used to derive a stochastic variant, which performs adaptive non-uniform sampling via the dual variables. | Ziwei Ji, Nathan Srebro, Matus Telgarsky | null | null | 2,021 | icml |
Marginalized Stochastic Natural Gradients for Black-Box Variational Inference | null | Black-box variational inference algorithms use stochastic sampling to analyze diverse statistical models, like those expressed in probabilistic programming languages, without model-specific derivations. While the popular score-function estimator computes unbiased gradient estimates, its variance is often unacceptably large, especially in models with discrete latent variables. We propose a stochastic natural gradient estimator that is as broadly applicable and unbiased, but improves efficiency by exploiting the curvature of the variational bound, and provably reduces variance by marginalizing discrete latent variables. Our marginalized stochastic natural gradients have intriguing connections to classic coordinate ascent variational inference, but allow parallel updates of variational parameters, and provide superior convergence guarantees relative to naive Monte Carlo approximations. We integrate our method with the probabilistic programming language Pyro and evaluate real-world models of documents, images, networks, and crowd-sourcing. Compared to score-function estimators, we require far fewer Monte Carlo samples and consistently convergence orders of magnitude faster. | Geng Ji, Debora Sujono, Erik B Sudderth | null | null | 2,021 | icml |
Factor-analytic inverse regression for high-dimension, small-sample dimensionality reduction | null | Sufficient dimension reduction (SDR) methods are a family of supervised methods for dimensionality reduction that seek to reduce dimensionality while preserving information about a target variable of interest. However, existing SDR methods typically require more observations than the number of dimensions ($N > p$). To overcome this limitation, we propose Class-conditional Factor Analytic Dimensions (CFAD), a model-based dimensionality reduction method for high-dimensional, small-sample data. We show that CFAD substantially outperforms existing SDR methods in the small-sample regime, and can be extended to incorporate prior information such as smoothness in the projection axes. We demonstrate the effectiveness of CFAD with an application to functional magnetic resonance imaging (fMRI) measurements during visual object recognition and working memory tasks, where it outperforms existing SDR and a variety of other dimensionality-reduction methods. | Aditi Jha, Michael J. Morais, Jonathan W Pillow | null | null | 2,021 | icml |
Multi-Dimensional Classification via Sparse Label Encoding | null | In multi-dimensional classification (MDC), there are multiple class variables in the output space with each of them corresponding to one heterogeneous class space. Due to the heterogeneity of class spaces, it is quite challenging to consider the dependencies among class variables when learning from MDC examples. In this paper, we propose a novel MDC approach named SLEM which learns the predictive model in an encoded label space instead of the original heterogeneous one. Specifically, SLEM works in an encoding-training-decoding framework. In the encoding phase, each class vector is mapped into a real-valued one via three cascaded operations including pairwise grouping, one-hot conversion and sparse linear encoding. In the training phase, a multi-output regression model is learned within the encoded label space. In the decoding phase, the predicted class vector is obtained by adapting orthogonal matching pursuit over outputs of the learned multi-output regression model. Experimental results clearly validate the superiority of SLEM against state-of-the-art MDC approaches. | Bin-Bin Jia, Min-Ling Zhang | null | null | 2,021 | icml |
Objective Bound Conditional Gaussian Process for Bayesian Optimization | null | A Gaussian process is a standard surrogate model for an unknown objective function in Bayesian optimization. In this paper, we propose a new surrogate model, called the objective bound conditional Gaussian process (OBCGP), to condition a Gaussian process on a bound on the optimal function value. The bound is obtained and updated as the best observed value during the sequential optimization procedure. Unlike the standard Gaussian process, the OBCGP explicitly incorporates the existence of a point that improves the best known bound. We treat the location of such a point as a model parameter and estimate it jointly with other parameters by maximizing the likelihood using variational inference. Within the standard Bayesian optimization framework, the OBCGP can be combined with various acquisition functions to select the next query point. In particular, we derive cumulative regret bounds for the OBCGP combined with the upper confidence bound acquisition algorithm. Furthermore, the OBCGP can inherently incorporate a new type of prior knowledge, i.e., the bounds on the optimum, if it is available. The incorporation of this type of prior knowledge into a surrogate model has not been studied previously. We demonstrate the effectiveness of the OBCGP through its application to Bayesian optimization tasks, such as the sequential design of experiments and hyperparameter optimization in neural networks. | Taewon Jeong, Heeyoung Kim | null | null | 2,021 | icml |
Catastrophic Fisher Explosion: Early Phase Fisher Matrix Impacts Generalization | null | The early phase of training a deep neural network has a dramatic effect on the local curvature of the loss function. For instance, using a small learning rate does not guarantee stable optimization because the optimization trajectory has a tendency to steer towards regions of the loss surface with increasing local curvature. We ask whether this tendency is connected to the widely observed phenomenon that the choice of the learning rate strongly influences generalization. We first show that stochastic gradient descent (SGD) implicitly penalizes the trace of the Fisher Information Matrix (FIM), a measure of the local curvature, from the start of training. We argue it is an implicit regularizer in SGD by showing that explicitly penalizing the trace of the FIM can significantly improve generalization. We highlight that poor final generalization coincides with the trace of the FIM attaining a large value early in training, to which we refer as catastrophic Fisher explosion. Finally, to gain insight into the regularization effect of penalizing the trace of the FIM, we show that it limits memorization by reducing the learning speed of examples with noisy labels more than that of the examples with clean labels. | Stanislaw Jastrzebski, Devansh Arpit, Oliver Astrand, Giancarlo B Kerg, Huan Wang, Caiming Xiong, Richard Socher, Kyunghyun Cho, Krzysztof J Geras | null | null | 2,021 | icml |
Efficient Statistical Tests: A Neural Tangent Kernel Approach | null | For machine learning models to make reliable predictions in deployment, one needs to ensure the previously unknown test samples need to be sufficiently similar to the training data. The commonly used shift-invariant kernels do not have the compositionality and fail to capture invariances in high-dimensional data in computer vision. We propose a shift-invariant convolutional neural tangent kernel (SCNTK) based outlier detector and two-sample tests with maximum mean discrepancy (MMD) that is O(n) in the number of samples due to using the random feature approximation. On MNIST and CIFAR10 with various types of dataset shifts, we empirically show that statistical tests with such compositional kernels, inherited from infinitely wide neural networks, achieve higher detection accuracy than existing non-parametric methods. Our method also provides a competitive alternative to adapted kernel methods that require a training phase. | Sheng Jia, Ehsan Nezhadarya, Yuhuai Wu, Jimmy Ba | null | null | 2,021 | icml |
Approximation Theory of Convolutional Architectures for Time Series Modelling | null | We study the approximation properties of convolutional architectures applied to time series modelling, which can be formulated mathematically as a functional approximation problem. In the recurrent setting, recent results reveal an intricate connection between approximation efficiency and memory structures in the data generation process. In this paper, we derive parallel results for convolutional architectures, with WaveNet being a prime example. Our results reveal that in this new setting, approximation efficiency is not only characterised by memory, but also additional fine structures in the target relationship. This leads to a novel definition of spectrum-based regularity that measures the complexity of temporal relationships under the convolutional approximation scheme. These analyses provide a foundation to understand the differences between architectural choices for time series modelling and can give theoretically grounded guidance for practical applications. | Haotian Jiang, Zhong Li, Qianxiao Li | null | null | 2,021 | icml |
Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision | null | Pre-trained representations are becoming crucial for many NLP and perception tasks. While representation learning in NLP has transitioned to training on raw text without human annotations, visual and vision-language representations still rely heavily on curated training datasets that are expensive or require expert knowledge. For vision applications, representations are mostly learned using datasets with explicit class labels such as ImageNet or OpenImages. For vision-language, popular datasets like Conceptual Captions, MSCOCO, or CLIP all involve a non-trivial data collection (and cleaning) process. This costly curation process limits the size of datasets and hence hinders the scaling of trained models. In this paper, we leverage a noisy dataset of over one billion image alt-text pairs, obtained without expensive filtering or post-processing steps in the Conceptual Captions dataset. A simple dual-encoder architecture learns to align visual and language representations of the image and text pairs using a contrastive loss. We show that the scale of our corpus can make up for its noise and leads to state-of-the-art representations even with such a simple learning scheme. Our visual representation achieves strong performance when transferred to classification tasks such as ImageNet and VTAB. The aligned visual and language representations enables zero-shot image classification and also set new state-of-the-art results on Flickr30K and MSCOCO image-text retrieval benchmarks, even when compared with more sophisticated cross-attention models. The representations also enable cross-modality search with complex text and text + image queries. | Chao Jia, Yinfei Yang, Ye Xia, Yi-Ting Chen, Zarana Parekh, Hieu Pham, Quoc Le, Yun-Hsuan Sung, Zhen Li, Tom Duerig | null | null | 2,021 | icml |
Self-Damaging Contrastive Learning | null | The recent breakthrough achieved by contrastive learning accelerates the pace for deploying unsupervised training on real-world data applications. However, unlabeled data in reality is commonly imbalanced and shows a long-tail distribution, and it is unclear how robustly the latest contrastive learning methods could perform in the practical scenario. This paper proposes to explicitly tackle this challenge, via a principled framework called Self-Damaging Contrastive Learning (SDCLR), to automatically balance the representation learning without knowing the classes. Our main inspiration is drawn from the recent finding that deep models have difficult-to-memorize samples, and those may be exposed through network pruning. It is further natural to hypothesize that long-tail samples are also tougher for the model to learn well due to insufficient examples. Hence, the key innovation in SDCLR is to create a dynamic self-competitor model to contrast with the target model, which is a pruned version of the latter. During training, contrasting the two models will lead to adaptive online mining of the most easily forgotten samples for the current target model, and implicitly emphasize them more in the contrastive loss. Extensive experiments across multiple datasets and imbalance settings show that SDCLR significantly improves not only overall accuracies but also balancedness, in terms of linear evaluation on the full-shot and few-shot settings. Our code is available at https://github.com/VITA-Group/SDCLR. | Ziyu Jiang, Tianlong Chen, Bobak J Mortazavi, Zhangyang Wang | null | null | 2,021 | icml |
Monotonic Robust Policy Optimization with Model Discrepancy | null | State-of-the-art deep reinforcement learning (DRL) algorithms tend to overfit due to the model discrepancy between source and target environments. Though applying domain randomization during training can improve the average performance by randomly generating a sufficient diversity of environments in simulator, the worst-case environment is still neglected without any performance guarantee. Since the average and worst-case performance are both important for generalization in RL, in this paper, we propose a policy optimization approach for concurrently improving the policy’s performance in the average and worst-case environment. We theoretically derive a lower bound for the worst-case performance of a given policy by relating it to the expected performance. Guided by this lower bound, we formulate an optimization problem to jointly optimize the policy and sampling distribution, and prove that by iteratively solving it the worst-case performance is monotonically improved. We then develop a practical algorithm, named monotonic robust policy optimization (MRPO). Experimental evaluations in several robot control tasks demonstrate that MRPO can generally improve both the average and worst-case performance in the source environments for training, and facilitate in all cases the learned policy with a better generalization capability in some unseen testing environments. | Yuankun Jiang, Chenglin Li, Wenrui Dai, Junni Zou, Hongkai Xiong | null | null | 2,021 | icml |
Almost Optimal Anytime Algorithm for Batched Multi-Armed Bandits | null | In batched multi-armed bandit problems, the learner can adaptively pull arms and adjust strategy in batches. In many real applications, not only the regret but also the batch complexity need to be optimized. Existing batched bandit algorithms usually assume that the time horizon T is known in advance. However, many applications involve an unpredictable stopping time. In this paper, we study the anytime batched multi-armed bandit problem. We propose an anytime algorithm that achieves the asymptotically optimal regret for exponential families of reward distributions with $O(\log \log T \ilog^{\alpha} (T))$ \footnote{Notation \ilog^{\alpha} (T) is the result of iteratively applying the logarithm function on T for \alpha times, e.g., \ilog^{3} (T)=\log\log\log T.} batches, where $\alpha\in O_{T}(1)$. Moreover, we prove that for any constant c>0, no algorithm can achieve the asymptotically optimal regret within c\log\log T batches. | Tianyuan Jin, Jing Tang, Pan Xu, Keke Huang, Xiaokui Xiao, Quanquan Gu | null | null | 2,021 | icml |
Streaming and Distributed Algorithms for Robust Column Subset Selection | null | We give the first single-pass streaming algorithm for Column Subset Selection with respect to the entrywise $\ell_p$-norm with $1 \leq p < 2$. We study the $\ell_p$ norm loss since it is often considered more robust to noise than the standard Frobenius norm. Given an input matrix $A \in \mathbb{R}^{d \times n}$ ($n \gg d$), our algorithm achieves a multiplicative $k^{\frac{1}{p} - \frac{1}{2}}\poly(\log nd)$-approximation to the error with respect to the \textit{best possible column subset} of size $k$. Furthermore, the space complexity of the streaming algorithm is optimal up to a logarithmic factor. Our streaming algorithm also extends naturally to a 1-round distributed protocol with nearly optimal communication cost. A key ingredient in our algorithms is a reduction to column subset selection in the $\ell_{p,2}$-norm, which corresponds to the $p$-norm of the vector of Euclidean norms of each of the columns of $A$. This enables us to leverage strong coreset constructions for the Euclidean norm, which previously had not been applied in this context. We also give the first provable guarantees for greedy column subset selection in the $\ell_{1, 2}$ norm, which can be used as an alternative, practical subroutine in our algorithms. Finally, we show that our algorithms give significant practical advantages on real-world data analysis tasks. | Shuli Jiang, Dennis Li, Irene Mengze Li, Arvind V Mahankali, David Woodruff | null | null | 2,021 | icml |
Online Selection Problems against Constrained Adversary | null | Inspired by a recent line of work in online algorithms with predictions, we study the constrained adversary model that utilizes predictions from a different perspective. Prior works mostly focused on designing simultaneously robust and consistent algorithms, without making assumptions on the quality of the predictions. In contrary, our model assumes the adversarial instance is consistent with the predictions and aim to design algorithms that have best worst-case performance against all such instances. We revisit classical online selection problems under the constrained adversary model. For the single item selection problem, we design an optimal algorithm in the adversarial arrival model and an improved algorithm in the random arrival model (a.k.a., the secretary problem). For the online edge-weighted bipartite matching problem, we extend the classical Water-filling and Ranking algorithms and achieve improved competitive ratios. | Zhihao Jiang, Pinyan Lu, Zhihao Gavin Tang, Yuhao Zhang | null | null | 2,021 | icml |
Characterizing Structural Regularities of Labeled Data in Overparameterized Models | null | Humans are accustomed to environments that contain both regularities and exceptions. For example, at most gas stations, one pays prior to pumping, but the occasional rural station does not accept payment in advance. Likewise, deep neural networks can generalize across instances that share common patterns or structures, yet have the capacity to memorize rare or irregular forms. We analyze how individual instances are treated by a model via a consistency score. The score characterizes the expected accuracy for a held-out instance given training sets of varying size sampled from the data distribution. We obtain empirical estimates of this score for individual instances in multiple data sets, and we show that the score identifies out-of-distribution and mislabeled examples at one end of the continuum and strongly regular examples at the other end. We identify computationally inexpensive proxies to the consistency score using statistics collected during training. We apply the score toward understanding the dynamics of representation learning and to filter outliers during training. | Ziheng Jiang, Chiyuan Zhang, Kunal Talwar, Michael C Mozer | null | null | 2,021 | icml |
Optimal Streaming Algorithms for Multi-Armed Bandits | null | This paper studies two variants of the best arm identification (BAI) problem under the streaming model, where we have a stream of n arms with reward distributions supported on [0,1] with unknown means. The arms in the stream are arriving one by one, and the algorithm cannot access an arm unless it is stored in a limited size memory. We first study the streaming \epslion-topk-arms identification problem, which asks for k arms whose reward means are lower than that of the k-th best arm by at most \epsilon with probability at least 1-\delta. For general \epsilon \in (0,1), the existing solution for this problem assumes k = 1 and achieves the optimal sample complexity O(\frac{n}{\epsilon^2} \log \frac{1}{\delta}) using O(\log^*(n)) memory and a single pass of the stream. We propose an algorithm that works for any k and achieves the optimal sample complexity O(\frac{n}{\epsilon^2} \log\frac{k}{\delta}) using a single-arm memory and a single pass of the stream. Second, we study the streaming BAI problem, where the objective is to identify the arm with the maximum reward mean with at least 1-\delta probability, using a single-arm memory and as few passes of the input stream as possible. We present a single-arm-memory algorithm that achieves a near instance-dependent optimal sample complexity within O(\log \Delta_2^{-1}) passes, where \Delta_2 is the gap between the mean of the best arm and that of the second best arm. | Tianyuan Jin, Keke Huang, Jing Tang, Xiaokui Xiao | null | null | 2,021 | icml |
Improved Confidence Bounds for the Linear Logistic Model and Applications to Bandits | null | We propose improved fixed-design confidence bounds for the linear logistic model. Our bounds significantly improve upon the state-of-the-art bound by Li et al. (2017) via recent developments of the self-concordant analysis of the logistic loss (Faury et al., 2020). Specifically, our confidence bound avoids a direct dependence on $1/\kappa$, where $\kappa$ is the minimal variance over all arms’ reward distributions. In general, $1/\kappa$ scales exponentially with the norm of the unknown linear parameter $\theta^*$. Instead of relying on this worst case quantity, our confidence bound for the reward of any given arm depends directly on the variance of that arm’s reward distribution. We present two applications of our novel bounds to pure exploration and regret minimization logistic bandits improving upon state-of-the-art performance guarantees. For pure exploration we also provide a lower bound highlighting a dependence on $1/\kappa$ for a family of instances. | Kwang-Sung Jun, Lalit Jain, Blake Mason, Houssam Nassif | null | null | 2,021 | icml |
Discrete-Valued Latent Preference Matrix Estimation with Graph Side Information | null | Incorporating graph side information into recommender systems has been widely used to better predict ratings, but relatively few works have focused on theoretical guarantees. Ahn et al. (2018) firstly characterized the optimal sample complexity in the presence of graph side information, but the results are limited due to strict, unrealistic assumptions made on the unknown latent preference matrix and the structure of user clusters. In this work, we propose a new model in which 1) the unknown latent preference matrix can have any discrete values, and 2) users can be clustered into multiple clusters, thereby relaxing the assumptions made in prior work. Under this new model, we fully characterize the optimal sample complexity and develop a computationally-efficient algorithm that matches the optimal sample complexity. Our algorithm is robust to model errors and outperforms the existing algorithms in terms of prediction performance on both synthetic and real data. | Changhun Jo, Kangwook Lee | null | null | 2,021 | icml |
Estimating Identifiable Causal Effects on Markov Equivalence Class through Double Machine Learning | null | General methods have been developed for estimating causal effects from observational data under causal assumptions encoded in the form of a causal graph. Most of this literature assumes that the underlying causal graph is completely specified. However, only observational data is available in most practical settings, which means that one can learn at most a Markov equivalence class (MEC) of the underlying causal graph. In this paper, we study the problem of causal estimation from a MEC represented by a partial ancestral graph (PAG), which is learnable from observational data. We develop a general estimator for any identifiable causal effects in a PAG. The result fills a gap for an end-to-end solution to causal inference from observational data to effects estimation. Specifically, we develop a complete identification algorithm that derives an influence function for any identifiable causal effects from PAGs. We then construct a double/debiased machine learning (DML) estimator that is robust to model misspecification and biases in nuisance function estimation, permitting the use of modern machine learning techniques. Simulation results corroborate with the theory. | Yonghan Jung, Jin Tian, Elias Bareinboim | null | null | 2,021 | icml |
The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation | null | We consider training models on private data that are distributed across user devices. To ensure privacy, we add on-device noise and use secure aggregation so that only the noisy sum is revealed to the server. We present a comprehensive end-to-end system, which appropriately discretizes the data and adds discrete Gaussian noise before performing secure aggregation. We provide a novel privacy analysis for sums of discrete Gaussians and carefully analyze the effects of data quantization and modular summation arithmetic. Our theoretical guarantees highlight the complex tension between communication, privacy, and accuracy. Our extensive experimental results demonstrate that our solution is essentially able to match the accuracy to central differential privacy with less than 16 bits of precision per value. | Peter Kairouz, Ziyu Liu, Thomas Steinke | null | null | 2,021 | icml |
On the Generalization Power of Overfitted Two-Layer Neural Tangent Kernel Models | null | In this paper, we study the generalization performance of min $\ell_2$-norm overfitting solutions for the neural tangent kernel (NTK) model of a two-layer neural network with ReLU activation that has no bias term. We show that, depending on the ground-truth function, the test error of overfitted NTK models exhibits characteristics that are different from the "double-descent" of other overparameterized linear models with simple Fourier or Gaussian features. Specifically, for a class of learnable functions, we provide a new upper bound of the generalization error that approaches a small limiting value, even when the number of neurons $p$ approaches infinity. This limiting value further decreases with the number of training samples $n$. For functions outside of this class, we provide a lower bound on the generalization error that does not diminish to zero even when $n$ and $p$ are both large. | Peizhong Ju, Xiaojun Lin, Ness Shroff | null | null | 2,021 | icml |
A Differentiable Point Process with Its Application to Spiking Neural Networks | null | This paper is concerned about a learning algorithm for a probabilistic model of spiking neural networks (SNNs). Jimenez Rezende & Gerstner (2014) proposed a stochastic variational inference algorithm to train SNNs with hidden neurons. The algorithm updates the variational distribution using the score function gradient estimator, whose high variance often impedes the whole learning algorithm. This paper presents an alternative gradient estimator for SNNs based on the path-wise gradient estimator. The main technical difficulty is a lack of a general method to differentiate a realization of an arbitrary point process, which is necessary to derive the path-wise gradient estimator. We develop a differentiable point process, which is the technical highlight of this paper, and apply it to derive the path-wise gradient estimator for SNNs. We investigate the effectiveness of our gradient estimator through numerical simulation. | Hiroshi Kajino | null | null | 2,021 | icml |
Training Recurrent Neural Networks via Forward Propagation Through Time | null | Back-propagation through time (BPTT) has been widely used for training Recurrent Neural Networks (RNNs). BPTT updates RNN parameters on an instance by back-propagating the error in time over the entire sequence length, and as a result, leads to poor trainability due to the well-known gradient explosion/decay phenomena. While a number of prior works have proposed to mitigate vanishing/explosion effect through careful RNN architecture design, these RNN variants still train with BPTT. We propose a novel forward-propagation algorithm, FPTT, where at each time, for an instance, we update RNN parameters by optimizing an instantaneous risk function. Our proposed risk is a regularization penalty at time $t$ that evolves dynamically based on previously observed losses, and allows for RNN parameter updates to converge to a stationary solution of the empirical RNN objective. We consider both sequence-to-sequence as well as terminal loss problems. Empirically FPTT outperforms BPTT on a number of well-known benchmark tasks, thus enabling architectures like LSTMs to solve long range dependencies problems. | Anil Kag, Venkatesh Saligrama | null | null | 2,021 | icml |
Practical and Private (Deep) Learning Without Sampling or Shuffling | null | We consider training models with differential privacy (DP) using mini-batch gradients. The existing state-of-the-art, Differentially Private Stochastic Gradient Descent (DP-SGD), requires \emph{privacy amplification by sampling or shuffling} to obtain the best privacy/accuracy/computation trade-offs. Unfortunately, the precise requirements on exact sampling and shuffling can be hard to obtain in important practical scenarios, particularly federated learning (FL). We design and analyze a DP variant of Follow-The-Regularized-Leader (DP-FTRL) that compares favorably (both theoretically and empirically) to amplified DP-SGD, while allowing for much more flexible data access patterns. DP-FTRL does not use any form of privacy amplification. | Peter Kairouz, Brendan Mcmahan, Shuang Song, Om Thakkar, Abhradeep Thakurta, Zheng Xu | null | null | 2,021 | icml |
Projection techniques to update the truncated SVD of evolving matrices with applications | null | This submission considers the problem of updating the rank-$k$ truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel in applications such as Latent Semantic Indexing and Recommender Systems. Nonetheless, the proposed framework is purely algebraic and targets general updating problems. The algorithm presented in this paper undertakes a projection viewpoint and focuses on building a pair of subspaces which approximate the linear span of the sought singular vectors of the updated matrix. We discuss and analyze two different choices to form the projection subspaces. Results on matrices from real applications suggest that the proposed algorithm can lead to higher accuracy, especially for the singular triplets associated with the largest modulus singular values. Several practical details and key differences with other approaches are also discussed. | Vasileios Kalantzis, Georgios Kollias, Shashanka Ubaru, Athanasios N. Nikolakopoulos, Lior Horesh, Kenneth Clarkson | null | null | 2,021 | icml |
A Nullspace Property for Subspace-Preserving Recovery | null | Much of the theory for classical sparse recovery is based on conditions on the dictionary that are both necessary and sufficient (e.g., nullspace property) or only sufficient (e.g., incoherence and restricted isometry). In contrast, much of the theory for subspace-preserving recovery, the theoretical underpinnings for sparse subspace classification and clustering methods, is based on conditions on the subspaces and the data that are only sufficient (e.g., subspace incoherence and data inner-radius). This paper derives a necessary and sufficient condition for subspace-preserving recovery that is inspired by the classical nullspace property.Based on this novel condition, called here the subspace nullspace property, we derive equivalent characterizations that either admit a clear geometric interpretation that relates data distribution and subspace separation to the recovery success, or can be verified using a finite set of extreme points of a properly defined set. We further exploit these characterizations to derive new sufficient conditions, based on inner-radius and outer-radius measures and dual bounds, that generalize existing conditions and preserve the geometric interpretations. These results fill an important gap in the subspace-preserving recovery literature. | Mustafa D Kaba, Chong You, Daniel P Robinson, Enrique Mallada, Rene Vidal | null | null | 2,021 | icml |
Efficient Performance Bounds for Primal-Dual Reinforcement Learning from Demonstrations | null | We consider large-scale Markov decision processes with an unknown cost function and address the problem of learning a policy from a finite set of expert demonstrations. We assume that the learner is not allowed to interact with the expert and has no access to reinforcement signal of any kind. Existing inverse reinforcement learning methods come with strong theoretical guarantees, but are computationally expensive, while state-of-the-art policy optimization algorithms achieve significant empirical success, but are hampered by limited theoretical understanding. To bridge the gap between theory and practice, we introduce a novel bilinear saddle-point framework using Lagrangian duality. The proposed primal-dual viewpoint allows us to develop a model-free provably efficient algorithm through the lens of stochastic convex optimization. The method enjoys the advantages of simplicity of implementation, low memory requirements, and computational and sample complexities independent of the number of states. We further present an equivalent no-regret online-learning interpretation. | Angeliki Kamoutsi, Goran Banjac, John Lygeros | null | null | 2,021 | icml |
SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice for Scalable Gaussian Processes | null | State-of-the-art methods for scalable Gaussian processes use iterative algorithms, requiring fast matrix vector multiplies (MVMs) with the co-variance kernel. The Structured Kernel Interpolation (SKI) framework accelerates these MVMs by performing efficient MVMs on a grid and interpolating back to the original space. In this work, we develop a connection between SKI and the permutohedral lattice used for high-dimensional fast bilateral filtering. Using a sparse simplicial grid instead of a dense rectangular one, we can perform GP inference exponentially faster in the dimension than SKI. Our approach, Simplex-GP, enables scaling SKI to high dimensions, while maintaining strong predictive performance. We additionally provide a CUDA implementation of Simplex-GP, which enables significant GPU acceleration of MVM based inference. | Sanyam Kapoor, Marc Finzi, Ke Alexander Wang, Andrew Gordon Gordon Wilson | null | null | 2,021 | icml |
When Does Data Augmentation Help With Membership Inference Attacks? | null | Deep learning models often raise privacy concerns as they leak information about their training data. This leakage enables membership inference attacks (MIA) that can identify whether a data point was in a model’s training set. Research shows that some ’data augmentation’ mechanisms may reduce the risk by combatting a key factor increasing the leakage, overfitting. While many mechanisms exist, their effectiveness against MIAs and privacy properties have not been studied systematically. Employing two recent MIAs, we explore the lower bound on the risk in the absence of formal upper bounds. First, we evaluate 7 mechanisms and differential privacy, on three image classification tasks. We find that applying augmentation to increase the model’s utility does not mitigate the risk and protection comes with a utility penalty. Further, we also investigate why popular label smoothing mechanism consistently amplifies the risk. Finally, we propose ’loss-rank-correlation’ (LRC) metric to assess how similar the effects of different mechanisms are. This, for example, reveals the similarity of applying high-intensity augmentation against MIAs to simply reducing the training time. Our findings emphasize the utility-privacy trade-off and provide practical guidelines on using augmentation to manage the trade-off. | Yigitcan Kaya, Tudor Dumitras | null | null | 2,021 | icml |
Affine Invariant Analysis of Frank-Wolfe on Strongly Convex Sets | null | It is known that the Frank-Wolfe (FW) algorithm, which is affine covariant, enjoys faster convergence rates than $\mathcal{O}\left(1/K\right)$ when the constraint set is strongly convex. However, these results rely on norm-dependent assumptions, usually incurring non-affine invariant bounds, in contradiction with FW’s affine covariant property. In this work, we introduce new structural assumptions on the problem (such as the directional smoothness) and derive an affine invariant, norm-independent analysis of Frank-Wolfe. We show that our rates are better than any other known convergence rates of FW in this setting. Based on our analysis, we propose an affine invariant backtracking line-search. Interestingly, we show that typical backtracking line-searches using smoothness of the objective function present similar performances than its affine invariant counterpart, despite using affine dependent norms in the step size’s computation. | Thomas Kerdreux, Lewis Liu, Simon Lacoste-Julien, Damien Scieur | null | null | 2,021 | icml |
Improved Regret Bounds of Bilinear Bandits using Action Space Analysis | null | We consider the bilinear bandit problem where the learner chooses a pair of arms, each from two different action spaces of dimension $d_1$ and $d_2$, respectively. The learner then receives a reward whose expectation is a bilinear function of the two chosen arms with an unknown matrix parameter $\Theta^*\in\mathbb{R}^{d_1 \times d_2}$ with rank $r$. Despite abundant applications such as drug discovery, the optimal regret rate is unknown for this problem, though it was conjectured to be $\tilde O(\sqrt{d_1d_2(d_1+d_2)r T})$ by Jun et al. (2019) where $\tilde O$ ignores polylogarithmic factors in $T$. In this paper, we make progress towards closing the gap between the upper and lower bound on the optimal regret. First, we reject the conjecture above by proposing algorithms that achieve the regret $\tilde O(\sqrt{d_1 d_2 (d_1+d_2) T})$ using the fact that the action space dimension $O(d_1+d_2)$ is significantly lower than the matrix parameter dimension $O(d_1 d_2)$. Second, we additionally devise an algorithm with better empirical performance than previous algorithms. | Kyoungseok Jang, Kwang-Sung Jun, Se-Young Yun, Wanmo Kang | null | null | 2,021 | icml |
Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation | null | Density ratio estimation (DRE) is at the core of various machine learning tasks such as anomaly detection and domain adaptation. In the DRE literature, existing studies have extensively studied methods based on Bregman divergence (BD) minimization. However, when we apply the BD minimization with highly flexible models, such as deep neural networks, it tends to suffer from what we call train-loss hacking, which is a source of over-fitting caused by a typical characteristic of empirical BD estimators. In this paper, to mitigate train-loss hacking, we propose non-negative correction for empirical BD estimators. Theoretically, we confirm the soundness of the proposed method through a generalization error bound. In our experiments, the proposed methods show favorable performances in inlier-based outlier detection. | Masahiro Kato, Takeshi Teshima | null | null | 2,021 | icml |
Improving Predictors via Combination Across Diverse Task Categories | null | Predictor combination is the problem of improving a task predictor using predictors of other tasks when the forms of individual predictors are unknown. Previous work approached this problem by nonparametrically assessing predictor relationships based on their joint evaluations on a shared sample. This limits their application to cases where all predictors are defined on the same task category, e.g. all predictors estimate attributes of shoes. We present a new predictor combination algorithm that overcomes this limitation. Our algorithm aligns the heterogeneous domains of different predictors in a shared latent space to facilitate comparisons of predictors independently of the domains on which they are originally defined. We facilitate this by a new data alignment scheme that matches data distributions across task categories. Based on visual attribute ranking experiments on datasets that span diverse task categories (e.g. shoes and animals), we demonstrate that our approach often significantly improves the performances of the initial predictors. | Kwang In Kim | null | null | 2,021 | icml |
GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training | null | The great success of modern machine learning models on large datasets is contingent on extensive computational resources with high financial and environmental costs. One way to address this is by extracting subsets that generalize on par with the full data. In this work, we propose a general framework, GRAD-MATCH, which finds subsets that closely match the gradient of the \emph{training or validation} set. We find such subsets effectively using an orthogonal matching pursuit algorithm. We show rigorous theoretical and convergence guarantees of the proposed algorithm and, through our extensive experiments on real-world datasets, show the effectiveness of our proposed framework. We show that GRAD-MATCH significantly and consistently outperforms several recent data-selection algorithms and achieves the best accuracy-efficiency trade-off. GRAD-MATCH is available as a part of the CORDS toolkit: \url{https://github.com/decile-team/cords}. | Krishnateja Killamsetty, Durga S, Ganesh Ramakrishnan, Abir De, Rishabh Iyer | null | null | 2,021 | icml |
I-BERT: Integer-only BERT Quantization | null | Transformer based models, like BERT and RoBERTa, have achieved state-of-the-art results in many Natural Language Processing tasks. However, their memory footprint, inference latency, and power consumption are prohibitive efficient inference at the edge, and even at the data center. While quantization can be a viable solution for this, previous work on quantizing Transformer based models use floating-point arithmetic during inference, which cannot efficiently utilize integer-only logical units such as the recent Turing Tensor Cores, or traditional integer-only ARM processors. In this work, we propose I-BERT, a novel quantization scheme for Transformer based models that quantizes the entire inference with integer-only arithmetic. Based on lightweight integer-only approximation methods for nonlinear operations, e.g., GELU, Softmax, and Layer Normalization, I-BERT performs an end-to-end integer-only BERT inference without any floating point calculation. We evaluate our approach on GLUE downstream tasks using RoBERTa-Base/Large. We show that for both cases, I-BERT achieves similar (and slightly higher) accuracy as compared to the full-precision baseline. Furthermore, our preliminary implementation of I-BERT shows a speedup of 2.4- 4.0x for INT8 inference on a T4 GPU system as compared to FP32 inference. The framework has been developed in PyTorch and has been open-sourced. | Sehoon Kim, Amir Gholami, Zhewei Yao, Michael W. Mahoney, Kurt Keutzer | null | null | 2,021 | icml |
Prior Image-Constrained Reconstruction using Style-Based Generative Models | null | Obtaining a useful estimate of an object from highly incomplete imaging measurements remains a holy grail of imaging science. Deep learning methods have shown promise in learning object priors or constraints to improve the conditioning of an ill-posed imaging inverse problem. In this study, a framework for estimating an object of interest that is semantically related to a known prior image, is proposed. An optimization problem is formulated in the disentangled latent space of a style-based generative model, and semantically meaningful constraints are imposed using the disentangled latent representation of the prior image. Stable recovery from incomplete measurements with the help of a prior image is theoretically analyzed. Numerical experiments demonstrating the superior performance of our approach as compared to related methods are presented. | Varun A Kelkar, Mark Anastasio | null | null | 2,021 | icml |
Conditional Variational Autoencoder with Adversarial Learning for End-to-End Text-to-Speech | null | Several recent end-to-end text-to-speech (TTS) models enabling single-stage training and parallel sampling have been proposed, but their sample quality does not match that of two-stage TTS systems. In this work, we present a parallel end-to-end TTS method that generates more natural sounding audio than current two-stage models. Our method adopts variational inference augmented with normalizing flows and an adversarial training process, which improves the expressive power of generative modeling. We also propose a stochastic duration predictor to synthesize speech with diverse rhythms from input text. With the uncertainty modeling over latent variables and the stochastic duration predictor, our method expresses the natural one-to-many relationship in which a text input can be spoken in multiple ways with different pitches and rhythms. A subjective human evaluation (mean opinion score, or MOS) on the LJ Speech, a single speaker dataset, shows that our method outperforms the best publicly available TTS systems and achieves a MOS comparable to ground truth. | Jaehyeon Kim, Jungil Kong, Juhee Son | null | null | 2,021 | icml |
A Policy Gradient Algorithm for Learning to Learn in Multiagent Reinforcement Learning | null | A fundamental challenge in multiagent reinforcement learning is to learn beneficial behaviors in a shared environment with other simultaneously learning agents. In particular, each agent perceives the environment as effectively non-stationary due to the changing policies of other agents. Moreover, each agent is itself constantly learning, leading to natural non-stationarity in the distribution of experiences encountered. In this paper, we propose a novel meta-multiagent policy gradient theorem that directly accounts for the non-stationary policy dynamics inherent to multiagent learning settings. This is achieved by modeling our gradient updates to consider both an agent’s own non-stationary policy dynamics and the non-stationary policy dynamics of other agents in the environment. We show that our theoretically grounded approach provides a general solution to the multiagent learning problem, which inherently comprises all key aspects of previous state of the art approaches on this topic. We test our method on a diverse suite of multiagent benchmarks and demonstrate a more efficient ability to adapt to new agents as they learn than baseline methods across the full spectrum of mixed incentive, competitive, and cooperative domains. | Dong Ki Kim, Miao Liu, Matthew D Riemer, Chuangchuang Sun, Marwa Abdulhai, Golnaz Habibi, Sebastian Lopez-Cot, Gerald Tesauro, Jonathan How | null | null | 2,021 | icml |
Reward Identification in Inverse Reinforcement Learning | null | We study the problem of reward identifiability in the context of Inverse Reinforcement Learning (IRL). The reward identifiability question is critical to answer when reasoning about the effectiveness of using Markov Decision Processes (MDPs) as computational models of real world decision makers in order to understand complex decision making behavior and perform counterfactual reasoning. While identifiability has been acknowledged as a fundamental theoretical question in IRL, little is known about the types of MDPs for which rewards are identifiable, or even if there exist such MDPs. In this work, we formalize the reward identification problem in IRL and study how identifiability relates to properties of the MDP model. For deterministic MDP models with the MaxEntRL objective, we prove necessary and sufficient conditions for identifiability. Building on these results, we present efficient algorithms for testing whether or not an MDP model is identifiable. | Kuno Kim, Shivam Garg, Kirankumar Shiragur, Stefano Ermon | null | null | 2,021 | icml |
Off-Policy Confidence Sequences | null | We develop confidence bounds that hold uniformly over time for off-policy evaluation in the contextual bandit setting. These confidence sequences are based on recent ideas from martingale analysis and are non-asymptotic, non-parametric, and valid at arbitrary stopping times. We provide algorithms for computing these confidence sequences that strike a good balance between computational and statistical efficiency. We empirically demonstrate the tightness of our approach in terms of failure probability and width and apply it to the “gated deployment” problem of safely upgrading a production contextual bandit system. | Nikos Karampatziakis, Paul Mineiro, Aaditya Ramdas | null | null | 2,021 | icml |
ViLT: Vision-and-Language Transformer Without Convolution or Region Supervision | null | Vision-and-Language Pre-training (VLP) has improved performance on various joint vision-and-language downstream tasks. Current approaches to VLP heavily rely on image feature extraction processes, most of which involve region supervision (e.g., object detection) and the convolutional architecture (e.g., ResNet). Although disregarded in the literature, we find it problematic in terms of both (1) efficiency/speed, that simply extracting input features requires much more computation than the multimodal interaction steps; and (2) expressive power, as it is upper bounded to the expressive power of the visual embedder and its predefined visual vocabulary. In this paper, we present a minimal VLP model, Vision-and-Language Transformer (ViLT), monolithic in the sense that the processing of visual inputs is drastically simplified to just the same convolution-free manner that we process textual inputs. We show that ViLT is up to tens of times faster than previous VLP models, yet with competitive or better downstream task performance. Our code and pre-trained weights are available at https://github.com/dandelin/vilt. | Wonjae Kim, Bokyung Son, Ildoo Kim | null | null | 2,021 | icml |
Message Passing Adaptive Resonance Theory for Online Active Semi-supervised Learning | null | Active learning is widely used to reduce labeling effort and training time by repeatedly querying only the most beneficial samples from unlabeled data. In real-world problems where data cannot be stored indefinitely due to limited storage or privacy issues, the query selection and the model update should be performed as soon as a new data sample is observed. Various online active learning methods have been studied to deal with these challenges; however, there are difficulties in selecting representative query samples and updating the model efficiently without forgetting. In this study, we propose Message Passing Adaptive Resonance Theory (MPART) that learns the distribution and topology of input data online. Through message passing on the topological graph, MPART actively queries informative and representative samples, and continuously improves the classification performance using both labeled and unlabeled data. We evaluate our model in stream-based selective sampling scenarios with comparable query selection strategies, showing that MPART significantly outperforms competitive models. | Taehyeong Kim, Injune Hwang, Hyundo Lee, Hyunseo Kim, Won-Seok Choi, Joseph J Lim, Byoung-Tak Zhang | null | null | 2,021 | icml |
Inferring Latent Dynamics Underlying Neural Population Activity via Neural Differential Equations | null | An important problem in systems neuroscience is to identify the latent dynamics underlying neural population activity. Here we address this problem by introducing a low-dimensional nonlinear model for latent neural population dynamics using neural ordinary differential equations (neural ODEs), with noisy sensory inputs and Poisson spike train outputs. We refer to this as the Poisson Latent Neural Differential Equations (PLNDE) model. We apply the PLNDE framework to a variety of synthetic datasets, and show that it accurately infers the phase portraits and fixed points of nonlinear systems augmented to produce spike train data, including the FitzHugh-Nagumo oscillator, a 3-dimensional nonlinear spiral, and a nonlinear sensory decision-making model with attractor dynamics. Our model significantly outperforms existing methods at inferring single-trial neural firing rates and the corresponding latent trajectories that generated them, especially in the regime where the spike counts and number of trials are low. We then apply our model to multi-region neural population recordings from medial frontal cortex of rats performing an auditory decision-making task. Our model provides a general, interpretable framework for investigating the neural mechanisms of decision-making and other cognitive computations through the lens of dynamical systems. | Timothy D. Kim, Thomas Z. Luo, Jonathan W. Pillow, Carlos D. Brody | null | null | 2,021 | icml |
CLOCS: Contrastive Learning of Cardiac Signals Across Space, Time, and Patients | null | The healthcare industry generates troves of unlabelled physiological data. This data can be exploited via contrastive learning, a self-supervised pre-training method that encourages representations of instances to be similar to one another. We propose a family of contrastive learning methods, CLOCS, that encourages representations across space, time, \textit{and} patients to be similar to one another. We show that CLOCS consistently outperforms the state-of-the-art methods, BYOL and SimCLR, when performing a linear evaluation of, and fine-tuning on, downstream tasks. We also show that CLOCS achieves strong generalization performance with only 25% of labelled training data. Furthermore, our training procedure naturally generates patient-specific representations that can be used to quantify patient-similarity. | Dani Kiyasseh, Tingting Zhu, David A Clifton | null | null | 2,021 | icml |
Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and More | null | The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for large sets of objects. In this work we propose two effective log-linear time approximations of the cost matrix: First, a sparse approximation based on locality sensitive hashing (LSH) and, second, a Nystr{ö}m approximation with LSH-based sparse corrections, which we call locally corrected Nystr{ö}m (LCN). These approximations enable general log-linear time algorithms for entropy-regularized OT that perform well even for the complex, high-dimensional spaces common in deep learning. We analyse these approximations theoretically and evaluate them experimentally both directly and end-to-end as a component for real-world applications. Using our approximations for unsupervised word embedding alignment enables us to speed up a state-of-the-art method by a factor of 3 while also improving the accuracy by 3.1 percentage points without any additional model changes. For graph distance regression we propose the graph transport network (GTN), which combines graph neural networks (GNNs) with enhanced Sinkhorn. GTN outcompetes previous models by 48% and still scales log-linearly in the number of nodes. | Johannes Gasteiger, Marten Lienen, Stephan Günnemann | null | null | 2,021 | icml |
Evaluating Robustness of Predictive Uncertainty Estimation: Are Dirichlet-based Models Reliable? | null | Dirichlet-based uncertainty (DBU) models are a recent and promising class of uncertainty-aware models. DBU models predict the parameters of a Dirichlet distribution to provide fast, high-quality uncertainty estimates alongside with class predictions. In this work, we present the first large-scale, in-depth study of the robustness of DBU models under adversarial attacks. Our results suggest that uncertainty estimates of DBU models are not robust w.r.t. three important tasks: (1) indicating correctly and wrongly classified samples; (2) detecting adversarial examples; and (3) distinguishing between in-distribution (ID) and out-of-distribution (OOD) data. Additionally, we explore the first approaches to make DBU mod- els more robust. While adversarial training has a minor effect, our median smoothing based ap- proach significantly increases robustness of DBU models. | Anna-Kathrin Kopetzki, Bertrand Charpentier, Daniel Zügner, Sandhya Giri, Stephan Günnemann | null | null | 2,021 | icml |
One-sided Frank-Wolfe algorithms for saddle problems | null | We study a class of convex-concave saddle-point problems of the form $\min_x\max_y ⟨Kx,y⟩+f_{\cal P}(x)-h^*(y)$ where $K$ is a linear operator, $f_{\cal P}$ is the sum of a convex function $f$ with a Lipschitz-continuous gradient and the indicator function of a bounded convex polytope ${\cal P}$, and $h^\ast$ is a convex (possibly nonsmooth) function. Such problem arises, for example, as a Lagrangian relaxation of various discrete optimization problems. Our main assumptions are the existence of an efficient {\em linear minimization oracle} ($lmo$) for $f_{\cal P}$ and an efficient {\em proximal map} ($prox$) for $h^*$ which motivate the solution via a blend of proximal primal-dual algorithms and Frank-Wolfe algorithms. In case $h^*$ is the indicator function of a linear constraint and function $f$ is quadratic, we show a $O(1/n^2)$ convergence rate on the dual objective, requiring $O(n \log n)$ calls of $lmo$. If the problem comes from the constrained optimization problem $\min_{x\in\mathbb R^d}\{f_{\cal P}(x)\:|\:Ax-b=0\}$ then we additionally get bound $O(1/n^2)$ both on the primal gap and on the infeasibility gap. In the most general case, we show a $O(1/n)$ convergence rate of the primal-dual gap again requiring $O(n\log n)$ calls of $lmo$. To the best of our knowledge, this improves on the known convergence rates for the considered class of saddle-point problems. We show applications to labeling problems frequently appearing in machine learning and computer vision. | Vladimir Kolmogorov, Thomas Pock | null | null | 2,021 | icml |
"Hey, that’s not an ODE": Faster ODE Adjoints via Seminorms | null | Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential equation solver. A proposed step is accepted if its error, \emph{relative to some norm}, is sufficiently small; else it is rejected, the step is shrunk, and the process is repeated. Here, we demonstrate that the particular structure of the adjoint equations makes the usual choices of norm (such as $L^2$) unnecessarily stringent. By replacing it with a more appropriate (semi)norm, fewer steps are unnecessarily rejected and the backpropagation is made faster. This requires only minor code modifications. Experiments on a wide range of tasks—including time series, generative modeling, and physical control—demonstrate a median improvement of 40% fewer function evaluations. On some problems we see as much as 62% fewer function evaluations, so that the overall training time is roughly halved. | Patrick Kidger, Ricky T. Q. Chen, Terry J Lyons | null | null | 2,021 | icml |
Offline Reinforcement Learning with Fisher Divergence Critic Regularization | null | Many modern approaches to offline Reinforcement Learning (RL) utilize behavior regularization, typically augmenting a model-free actor critic algorithm with a penalty measuring divergence of the policy from the offline data. In this work, we propose an alternative approach to encouraging the learned policy to stay close to the data, namely parameterizing the critic as the log-behavior-policy, which generated the offline data, plus a state-action value offset term, which can be learned using a neural network. Behavior regularization then corresponds to an appropriate regularizer on the offset term. We propose using a gradient penalty regularizer for the offset term and demonstrate its equivalence to Fisher divergence regularization, suggesting connections to the score matching and generative energy-based model literature. We thus term our resulting algorithm Fisher-BRC (Behavior Regularized Critic). On standard offline RL benchmarks, Fisher-BRC achieves both improved performance and faster convergence over existing state-of-the-art methods. | Ilya Kostrikov, Rob Fergus, Jonathan Tompson, Ofir Nachum | null | null | 2,021 | icml |
A Lower Bound for the Sample Complexity of Inverse Reinforcement Learning | null | Inverse reinforcement learning (IRL) is the task of finding a reward function that generates a desired optimal policy for a given Markov Decision Process (MDP). This paper develops an information-theoretic lower bound for the sample complexity of the finite state, finite action IRL problem. A geometric construction of $\beta$-strict separable IRL problems using spherical codes is considered. Properties of the ensemble size as well as the Kullback-Leibler divergence between the generated trajectories are derived. The resulting ensemble is then used along with Fano’s inequality to derive a sample complexity lower bound of $O(n \log n)$, where $n$ is the number of states in the MDP. | Abi Komanduru, Jean Honorio | null | null | 2,021 | icml |
A Distribution-dependent Analysis of Meta Learning | null | A key problem in the theory of meta-learning is to understand how the task distributions influence transfer risk, the expected error of a meta-learner on a new task drawn from the unknown task distribution. In this paper, focusing on fixed design linear regression with Gaussian noise and a Gaussian task (or parameter) distribution, we give distribution-dependent lower bounds on the transfer risk of any algorithm, while we also show that a novel, weighted version of the so-called biased regularized regression method is able to match these lower bounds up to a fixed constant factor. Notably, the weighting is derived from the covariance of the Gaussian task distribution. Altogether, our results provide a precise characterization of the difficulty of meta-learning in this Gaussian setting. While this problem setting may appear simple, we show that it is rich enough to unify the “parameter sharing” and “representation learning” streams of meta-learning; in particular, representation learning is obtained as the special case when the covariance matrix of the task distribution is unknown. For this case we propose to adopt the EM method, which is shown to enjoy efficient updates in our case. The paper is completed by an empirical study of EM. In particular, our experimental results show that the EM algorithm can attain the lower bound as the number of tasks grows, while the algorithm is also successful in competing with its alternatives when used in a representation learning context. | Mikhail Konobeev, Ilja Kuzborskij, Csaba Szepesvari | null | null | 2,021 | icml |
ADOM: Accelerated Decentralized Optimization Method for Time-Varying Networks | null | We propose ADOM – an accelerated method for smooth and strongly convex decentralized optimization over time-varying networks. ADOM uses a dual oracle, i.e., we assume access to the gradient of the Fenchel conjugate of the individual loss functions. Up to a constant factor, which depends on the network structure only, its communication complexity is the same as that of accelerated Nesterov gradient method. To the best of our knowledge, only the algorithm of Rogozin et al. (2019) has a convergence rate with similar properties. However, their algorithm converges under the very restrictive assumption that the number of network changes can not be greater than a tiny percentage of the number of iterations. This assumption is hard to satisfy in practice, as the network topology changes usually can not be controlled. In contrast, ADOM merely requires the network to stay connected throughout time. | Dmitry Kovalev, Egor Shulgin, Peter Richtarik, Alexander V Rogozin, Alexander Gasnikov | null | null | 2,021 | icml |
Boosting the Throughput and Accelerator Utilization of Specialized CNN Inference Beyond Increasing Batch Size | null | Datacenter vision systems widely use small, specialized convolutional neural networks (CNNs) trained on specific tasks for high-throughput inference. These settings employ accelerators with massive computational capacity, but which specialized CNNs underutilize due to having low arithmetic intensity. This results in suboptimal application-level throughput and poor returns on accelerator investment. Increasing batch size is the only known way to increase both application-level throughput and accelerator utilization for inference, but yields diminishing returns; specialized CNNs poorly utilize accelerators even with large batch size. We propose FoldedCNNs, a new approach to CNN design that increases inference throughput and utilization beyond large batch size. FoldedCNNs rethink the structure of inputs and layers of specialized CNNs to boost arithmetic intensity: in FoldedCNNs, f images with C channels each are concatenated into a single input with fC channels and jointly classified by a wider CNN. Increased arithmetic intensity in FoldedCNNs increases the throughput and GPU utilization of specialized CNN inference by up to 2.5x and 2.8x, with accuracy close to the original CNN in most cases. | Jack Kosaian, Amar Phanishayee, Matthai Philipose, Debadeepta Dey, Rashmi Vinayak | null | null | 2,021 | icml |
Adapting to misspecification in contextual bandits with offline regression oracles | null | Computationally efficient contextual bandits are often based on estimating a predictive model of rewards given contexts and arms using past data. However, when the reward model is not well-specified, the bandit algorithm may incur unexpected regret, so recent work has focused on algorithms that are robust to misspecification. We propose a simple family of contextual bandit algorithms that adapt to misspecification error by reverting to a good safe policy when there is evidence that misspecification is causing a regret increase. Our algorithm requires only an offline regression oracle to ensure regret guarantees that gracefully degrade in terms of a measure of the average misspecification level. Compared to prior work, we attain similar regret guarantees, but we do no rely on a master algorithm, and do not require more robust oracles like online or constrained regression oracles (e.g., Foster et al. (2020), Krishnamurthy et al. (2020)). This allows us to design algorithms for more general function approximation classes. | Sanath Kumar Krishnamurthy, Vitor Hadad, Susan Athey | null | null | 2,021 | icml |
Bayesian Structural Adaptation for Continual Learning | null | Continual Learning is a learning paradigm where learning systems are trained on a sequence of tasks. The goal here is to perform well on the current task without suffering from a performance drop on the previous tasks. Two notable directions among the recent advances in continual learning with neural networks are (1) variational Bayes based regularization by learning priors from previous tasks, and, (2) learning the structure of deep networks to adapt to new tasks. So far, these two approaches have been largely orthogonal. We present a novel Bayesian framework based on continually learning the structure of deep neural networks, to unify these distinct yet complementary approaches. The proposed framework learns the deep structure for each task by learning which weights to be used, and supports inter-task transfer through the overlapping of different sparse subsets of weights learned by different tasks. An appealing aspect of our proposed continual learning framework is that it is applicable to both discriminative (supervised) and generative (unsupervised) settings. Experimental results on supervised and unsupervised benchmarks demonstrate that our approach performs comparably or better than recent advances in continual learning. | Abhishek Kumar, Sunabha Chatterjee, Piyush Rai | null | null | 2,021 | icml |
High Confidence Generalization for Reinforcement Learning | null | We present several classes of reinforcement learning algorithms that safely generalize to Markov decision processes (MDPs) not seen during training. Specifically, we study the setting in which some set of MDPs is accessible for training. The goal is to generalize safely to MDPs that are sampled from the same distribution, but which may not be in the set accessible for training. For various definitions of safety, our algorithms give probabilistic guarantees that agents can safely generalize to MDPs that are sampled from the same distribution but are not necessarily in the training set. These algorithms are a type of Seldonian algorithm (Thomas et al., 2019), which is a class of machine learning algorithms that return models with probabilistic safety guarantees for user-specified definitions of safety. | James Kostas, Yash Chandak, Scott M Jordan, Georgios Theocharous, Philip Thomas | null | null | 2,021 | icml |
Targeted Data Acquisition for Evolving Negotiation Agents | null | Successful negotiators must learn how to balance optimizing for self-interest and cooperation. Yet current artificial negotiation agents often heavily depend on the quality of the static datasets they were trained on, limiting their capacity to fashion an adaptive response balancing self-interest and cooperation. For this reason, we find that these agents can achieve either high utility or cooperation, but not both. To address this, we introduce a targeted data acquisition framework where we guide the exploration of a reinforcement learning agent using annotations from an expert oracle. The guided exploration incentivizes the learning agent to go beyond its static dataset and develop new negotiation strategies. We show that this enables our agents to obtain higher-reward and more Pareto-optimal solutions when negotiating with both simulated and human partners compared to standard supervised learning and reinforcement learning methods. This trend additionally holds when comparing agents using our targeted data acquisition framework to variants of agents trained with a mix of supervised learning and reinforcement learning, or to agents using tailored reward functions that explicitly optimize for utility and Pareto-optimality. | Minae Kwon, Siddharth Karamcheti, Mariano-Florentino Cuellar, Dorsa Sadigh | null | null | 2,021 | icml |
Implicit rate-constrained optimization of non-decomposable objectives | null | We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest. Examples of such problems include optimizing false negative rate at a fixed false positive rate, optimizing precision at a fixed recall, optimizing the area under the precision-recall or ROC curves, etc. Our key idea is to formulate a rate-constrained optimization that expresses the threshold parameter as a function of the model parameters via the Implicit Function theorem. We show how the resulting optimization problem can be solved using standard gradient based methods. Experiments on benchmark datasets demonstrate the effectiveness of our proposed method over existing state-of-the-art approaches for these problems. | Abhishek Kumar, Harikrishna Narasimhan, Andrew Cotter | null | null | 2,021 | icml |
ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks | null | Recently, learning algorithms motivated from sharpness of loss surface as an effective measure of generalization gap have shown state-of-the-art performances. Nevertheless, sharpness defined in a rigid region with a fixed radius, has a drawback in sensitivity to parameter re-scaling which leaves the loss unaffected, leading to weakening of the connection between sharpness and generalization gap. In this paper, we introduce the concept of adaptive sharpness which is scale-invariant and propose the corresponding generalization bound. We suggest a novel learning method, adaptive sharpness-aware minimization (ASAM), utilizing the proposed generalization bound. Experimental results in various benchmark datasets show that ASAM contributes to significant improvement of model generalization performance. | Jungmin Kwon, Jeongseop Kim, Hyunseo Park, In Kwon Choi | null | null | 2,021 | icml |
Efficient Message Passing for 0–1 ILPs with Binary Decision Diagrams | null | We present a message passing method for 0{–}1 integer linear programs. Our algorithm is based on a decomposition of the original problem into subproblems that are represented as binary deci- sion diagrams. The resulting Lagrangean dual is solved iteratively by a series of efficient block coordinate ascent steps. Our method has linear iteration complexity in the size of the decomposi- tion and can be effectively parallelized. The char- acteristics of our approach are desirable towards solving ever larger problems arising in structured prediction. We present experimental results on combinatorial problems from MAP inference for Markov Random Fields, quadratic assignment, discrete tomography and cell tracking for develop- mental biology and show promising performance. | Jan-Hendrik Lange, Paul Swoboda | null | null | 2,021 | icml |
Revisiting Peng’s Q($λ$) for Modern Reinforcement Learning | null | Off-policy multi-step reinforcement learning algorithms consist of conservative and non-conservative algorithms: the former actively cut traces, whereas the latter do not. Recently, Munos et al. (2016) proved the convergence of conservative algorithms to an optimal Q-function. In contrast, non-conservative algorithms are thought to be unsafe and have a limited or no theoretical guarantee. Nonetheless, recent studies have shown that non-conservative algorithms empirically outperform conservative ones. Motivated by the empirical results and the lack of theory, we carry out theoretical analyses of Peng’s Q($\lambda$), a representative example of non-conservative algorithms. We prove that \emph{it also converges to an optimal policy} provided that the behavior policy slowly tracks a greedy policy in a way similar to conservative policy iteration. Such a result has been conjectured to be true but has not been proven. We also experiment with Peng’s Q($\lambda$) in complex continuous control tasks, confirming that Peng’s Q($\lambda$) often outperforms conservative algorithms despite its simplicity. These results indicate that Peng’s Q($\lambda$), which was thought to be unsafe, is a theoretically-sound and practically effective algorithm. | Tadashi Kozuno, Yunhao Tang, Mark Rowland, Remi Munos, Steven Kapturowski, Will Dabney, Michal Valko, David Abel | null | null | 2,021 | icml |
Gradient Disaggregation: Breaking Privacy in Federated Learning by Reconstructing the User Participant Matrix | null | We show that aggregated model updates in federated learning may be insecure. An untrusted central server may disaggregate user updates from sums of updates across participants given repeated observations, enabling the server to recover privileged information about individual users’ private training data via traditional gradient inference attacks. Our method revolves around reconstructing participant information (e.g: which rounds of training users participated in) from aggregated model updates by leveraging summary information from device analytics commonly used to monitor, debug, and manage federated learning systems. Our attack is parallelizable and we successfully disaggregate user updates on settings with up to thousands of participants. We quantitatively and qualitatively demonstrate significant improvements in the capability of various inference attacks on the disaggregated updates. Our attack enables the attribution of learned properties to individual users, violating anonymity, and shows that a determined central server may undermine the secure aggregation protocol to break individual users’ data privacy in federated learning. | Maximilian Lam, Gu-Yeon Wei, David Brooks, Vijay Janapa Reddi, Michael Mitzenmacher | null | null | 2,021 | icml |
Adaptive Newton Sketch: Linear-time Optimization with Quadratic Convergence and Effective Hessian Dimensionality | null | We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a random projection of the Hessian. Our first contribution is to show that, at each iteration, the embedding dimension (or sketch size) can be as small as the effective dimension of the Hessian matrix. Leveraging this novel fundamental result, we design an algorithm with a sketch size proportional to the effective dimension and which exhibits a quadratic rate of convergence. This result dramatically improves on the classical linear-quadratic convergence rates of state-of-the-art sub-sampled Newton methods. However, in most practical cases, the effective dimension is not known beforehand, and this raises the question of how to pick a sketch size as small as the effective dimension while preserving a quadratic convergence rate. Our second and main contribution is thus to propose an adaptive sketch size algorithm with quadratic convergence rate and which does not require prior knowledge or estimation of the effective dimension: at each iteration, it starts with a small sketch size, and increases it until quadratic progress is achieved. Importantly, we show that the embedding dimension remains proportional to the effective dimension throughout the entire path and that our method achieves state-of-the-art computational complexity for solving convex optimization programs with a strongly convex component. We discuss and illustrate applications to linear and quadratic programming, as well as logistic regression and other generalized linear models. | Jonathan Lacotte, Yifei Wang, Mert Pilanci | null | null | 2,021 | icml |
Sharing Less is More: Lifelong Learning in Deep Networks with Selective Layer Transfer | null | Effective lifelong learning across diverse tasks requires the transfer of diverse knowledge, yet transferring irrelevant knowledge may lead to interference and catastrophic forgetting. In deep networks, transferring the appropriate granularity of knowledge is as important as the transfer mechanism, and must be driven by the relationships among tasks. We first show that the lifelong learning performance of several current deep learning architectures can be significantly improved by transfer at the appropriate layers. We then develop an expectation-maximization (EM) method to automatically select the appropriate transfer configuration and optimize the task network weights. This EM-based selective transfer is highly effective, balancing transfer performance on all tasks with avoiding catastrophic forgetting, as demonstrated on three algorithms in several lifelong object classification scenarios. | Seungwon Lee, Sima Behpour, Eric Eaton | null | null | 2,021 | icml |
Model Fusion for Personalized Learning | null | Production systems operating on a growing domain of analytic services often require generating warm-start solution models for emerging tasks with limited data. One potential approach to address this warm-start challenge is to adopt meta learning to generate a base model that can be adapted to solve unseen tasks with minimal fine-tuning. This however requires the training processes of previous solution models of existing tasks to be synchronized. This is not possible if these models were pre-trained separately on private data owned by different entities and cannot be synchronously re-trained. To accommodate for such scenarios, we develop a new personalized learning framework that synthesizes customized models for unseen tasks via fusion of independently pre-trained models of related tasks. We establish performance guarantee for the proposed framework and demonstrate its effectiveness on both synthetic and real datasets. | Thanh Chi Lam, Nghia Hoang, Bryan Kian Hsiang Low, Patrick Jaillet | null | null | 2,021 | icml |
Fair Selective Classification Via Sufficiency | null | Selective classification is a powerful tool for decision-making in scenarios where mistakes are costly but abstentions are allowed. In general, by allowing a classifier to abstain, one can improve the performance of a model at the cost of reducing coverage and classifying fewer samples. However, recent work has shown, in some cases, that selective classification can magnify disparities between groups, and has illustrated this phenomenon on multiple real-world datasets. We prove that the sufficiency criterion can be used to mitigate these disparities by ensuring that selective classification increases performance on all groups, and introduce a method for mitigating the disparity in precision across the entire coverage scale based on this criterion. We then provide an upper bound on the conditional mutual information between the class label and sensitive attribute, conditioned on the learned features, which can be used as a regularizer to achieve fairer selective classification. The effectiveness of the method is demonstrated on the Adult, CelebA, Civil Comments, and CheXpert datasets. | Joshua K Lee, Yuheng Bu, Deepta Rajan, Prasanna Sattigeri, Rameswar Panda, Subhro Das, Gregory W Wornell | null | null | 2,021 | icml |
Gaussian Process-Based Real-Time Learning for Safety Critical Applications | null | The safe operation of physical systems typically relies on high-quality models. Since a continuous stream of data is generated during run-time, such models are often obtained through the application of Gaussian process regression because it provides guarantees on the prediction error. Due to its high computational complexity, Gaussian process regression must be used offline on batches of data, which prevents applications, where a fast adaptation through online learning is necessary to ensure safety. In order to overcome this issue, we propose the LoG-GP. It achieves a logarithmic update and prediction complexity in the number of training points through the aggregation of locally active Gaussian process models. Under weak assumptions on the aggregation scheme, it inherits safety guarantees from exact Gaussian process regression. These theoretical advantages are exemplarily exploited in the design of a safe and data-efficient, online-learning control policy. The efficiency and performance of the proposed real-time learning approach is demonstrated in a comparison to state-of-the-art methods. | Armin Lederer, Alejandro J Ordóñez Conejo, Korbinian A Maier, Wenxin Xiao, Jonas Umlauft, Sandra Hirche | null | null | 2,021 | icml |
MorphVAE: Generating Neural Morphologies from 3D-Walks using a Variational Autoencoder with Spherical Latent Space | null | For the past century, the anatomy of a neuron has been considered one of its defining features: The shape of a neuron’s dendrites and axon fundamentally determines what other neurons it can connect to. These neurites have been described using mathematical tools e.g. in the context of cell type classification, but generative models of these structures have only rarely been proposed and are often computationally inefficient. Here we propose MorphVAE, a sequence-to-sequence variational autoencoder with spherical latent space as a generative model for neural morphologies. The model operates on walks within the tree structure of a neuron and can incorporate expert annotations on a subset of the data using semi-supervised learning. We develop our model on artificially generated toy data and evaluate its performance on dendrites of excitatory cells and axons of inhibitory cells of mouse motor cortex (M1) and dendrites of retinal ganglion cells. We show that the learned latent feature space allows for better cell type discrimination than other commonly used features. By sampling new walks from the latent space we can easily construct new morphologies with a specified degree of similarity to their reference neuron, providing an efficient generative model for neural morphologies. | Sophie C. Laturnus, Philipp Berens | null | null | 2,021 | icml |
Unsupervised Embedding Adaptation via Early-Stage Feature Reconstruction for Few-Shot Classification | null | We propose unsupervised embedding adaptation for the downstream few-shot classification task. Based on findings that deep neural networks learn to generalize before memorizing, we develop Early-Stage Feature Reconstruction (ESFR) — a novel adaptation scheme with feature reconstruction and dimensionality-driven early stopping that finds generalizable features. Incorporating ESFR consistently improves the performance of baseline methods on all standard settings, including the recently proposed transductive method. ESFR used in conjunction with the transductive method further achieves state-of-the-art performance on mini-ImageNet, tiered-ImageNet, and CUB; especially with 1.2% 2.0% improvements in accuracy over the previous best performing method on 1-shot setting. | Dong Hoon Lee, Sae-Young Chung | null | null | 2,021 | icml |
On-the-fly Rectification for Robust Large-Vocabulary Topic Inference | null | Across many data domains, co-occurrence statistics about the joint appearance of objects are powerfully informative. By transforming unsupervised learning problems into decompositions of co-occurrence statistics, spectral algorithms provide transparent and efficient algorithms for posterior inference such as latent topic analysis and community detection. As object vocabularies grow, however, it becomes rapidly more expensive to store and run inference algorithms on co-occurrence statistics. Rectifying co-occurrence, the key process to uphold model assumptions, becomes increasingly more vital in the presence of rare terms, but current techniques cannot scale to large vocabularies. We propose novel methods that simultaneously compress and rectify co-occurrence statistics, scaling gracefully with the size of vocabulary and the dimension of latent space. We also present new algorithms learning latent variables from the compressed statistics, and verify that our methods perform comparably to previous approaches on both textual and non-textual data. | Moontae Lee, Sungjun Cho, Kun Dong, David Mimno, David Bindel | null | null | 2,021 | icml |
Graph Cuts Always Find a Global Optimum for Potts Models (With a Catch) | null | We prove that the alpha-expansion algorithm for MAP inference always returns a globally optimal assignment for Markov Random Fields with Potts pairwise potentials, with a catch: the returned assignment is only guaranteed to be optimal for an instance within a small perturbation of the original problem instance. In other words, all local minima with respect to expansion moves are global minima to slightly perturbed versions of the problem. On "real-world" instances, MAP assignments of small perturbations of the problem should be very similar to the MAP assignment(s) of the original problem instance. We design an algorithm that can certify whether this is the case in practice. On several MAP inference problem instances from computer vision, this algorithm certifies that MAP solutions to all of these perturbations are very close to solutions of the original instance. These results taken together give a cohesive explanation for the good performance of "graph cuts" algorithms in practice. Every local expansion minimum is a global minimum in a small perturbation of the problem, and all of these global minima are close to the original solution. | Hunter Lang, David Sontag, Aravindan Vijayaraghavan | null | null | 2,021 | icml |
Achieving Near Instance-Optimality and Minimax-Optimality in Stochastic and Adversarial Linear Bandits Simultaneously | null | In this work, we develop linear bandit algorithms that automatically adapt to different environments. By plugging a novel loss estimator into the optimization problem that characterizes the instance-optimal strategy, our first algorithm not only achieves nearly instance-optimal regret in stochastic environments, but also works in corrupted environments with additional regret being the amount of corruption, while the state-of-the-art (Li et al., 2019) achieves neither instance-optimality nor the optimal dependence on the corruption amount. Moreover, by equipping this algorithm with an adversarial component and carefully-designed testings, our second algorithm additionally enjoys minimax-optimal regret in completely adversarial environments, which is the first of this kind to our knowledge. Finally, all our guarantees hold with high probability, while existing instance-optimal guarantees only hold in expectation. | Chung-Wei Lee, Haipeng Luo, Chen-Yu Wei, Mengxiao Zhang, Xiaojin Zhang | null | null | 2,021 | icml |
OptiDICE: Offline Policy Optimization via Stationary Distribution Correction Estimation | null | We consider the offline reinforcement learning (RL) setting where the agent aims to optimize the policy solely from the data without further environment interactions. In offline RL, the distributional shift becomes the primary source of difficulty, which arises from the deviation of the target policy being optimized from the behavior policy used for data collection. This typically causes overestimation of action values, which poses severe problems for model-free algorithms that use bootstrapping. To mitigate the problem, prior offline RL algorithms often used sophisticated techniques that encourage underestimation of action values, which introduces an additional set of hyperparameters that need to be tuned properly. In this paper, we present an offline RL algorithm that prevents overestimation in a more principled way. Our algorithm, OptiDICE, directly estimates the stationary distribution corrections of the optimal policy and does not rely on policy-gradients, unlike previous offline RL algorithms. Using an extensive set of benchmark datasets for offline RL, we show that OptiDICE performs competitively with the state-of-the-art methods. | Jongmin Lee, Wonseok Jeon, Byungjun Lee, Joelle Pineau, Kee-Eung Kim | null | null | 2,021 | icml |
Generalization Bounds in the Presence of Outliers: a Median-of-Means Study | null | In contrast to the empirical mean, the Median-of-Means (MoM) is an estimator of the mean $\theta$ of a square integrable r.v. Z, around which accurate nonasymptotic confidence bounds can be built, even when Z does not exhibit a sub-Gaussian tail behavior. Thanks to the high confidence it achieves on heavy-tailed data, MoM has found various applications in machine learning, where it is used to design training procedures that are not sensitive to atypical observations. More recently, a new line of work is now trying to characterize and leverage MoM’s ability to deal with corrupted data. In this context, the present work proposes a general study of MoM’s concentration properties under the contamination regime, that provides a clear understanding on the impact of the outlier proportion and the number of blocks chosen. The analysis is extended to (multisample) U-statistics, i.e. averages over tuples of observations, that raise additional challenges due to the dependence induced. Finally, we show that the latter bounds can be used in a straightforward fashion to derive generalization guarantees for pairwise learning in a contaminated setting, and propose an algorithm to compute provably reliable decision functions. | Pierre Laforgue, Guillaume Staerman, Stephan Clémençon | null | null | 2,021 | icml |
Continual Learning in the Teacher-Student Setup: Impact of Task Similarity | null | Continual learning{—}the ability to learn many tasks in sequence{—}is critical for artificial learning systems. Yet standard training methods for deep networks often suffer from catastrophic forgetting, where learning new tasks erases knowledge of the earlier tasks. While catastrophic forgetting labels the problem, the theoretical reasons for interference between tasks remain unclear. Here, we attempt to narrow this gap between theory and practice by studying continual learning in the teacher-student setup. We extend previous analytical work on two-layer networks in the teacher-student setup to multiple teachers. Using each teacher to represent a different task, we investigate how the relationship between teachers affects the amount of forgetting and transfer exhibited by the student when the task switches. In line with recent work, we find that when tasks depend on similar features, intermediate task similarity leads to greatest forgetting. However, feature similarity is only one way in which tasks may be related. The teacher-student approach allows us to disentangle task similarity at the level of \emph{readouts} (hidden-to-output weights) as well as \emph{features} (input-to-hidden weights). We find a complex interplay between both types of similarity, initial transfer/forgetting rates, maximum transfer/forgetting, and the long-time (post-switch) amount of transfer/forgetting. Together, these results help illuminate the diverse factors contributing to catastrophic forgetting. | Sebastian Lee, Sebastian Goldt, Andrew Saxe | null | null | 2,021 | icml |
SUNRISE: A Simple Unified Framework for Ensemble Learning in Deep Reinforcement Learning | null | Off-policy deep reinforcement learning (RL) has been successful in a range of challenging domains. However, standard off-policy RL algorithms can suffer from several issues, such as instability in Q-learning and balancing exploration and exploitation. To mitigate these issues, we present SUNRISE, a simple unified ensemble method, which is compatible with various off-policy RL algorithms. SUNRISE integrates two key ingredients: (a) ensemble-based weighted Bellman backups, which re-weight target Q-values based on uncertainty estimates from a Q-ensemble, and (b) an inference method that selects actions using the highest upper-confidence bounds for efficient exploration. By enforcing the diversity between agents using Bootstrap with random initialization, we show that these different ideas are largely orthogonal and can be fruitfully integrated, together further improving the performance of existing off-policy RL algorithms, such as Soft Actor-Critic and Rainbow DQN, for both continuous and discrete control tasks on both low-dimensional and high-dimensional environments. | Kimin Lee, Michael Laskin, Aravind Srinivas, Pieter Abbeel | null | null | 2,021 | icml |
LAMDA: Label Matching Deep Domain Adaptation | null | Deep domain adaptation (DDA) approaches have recently been shown to perform better than their shallow rivals with better modeling capacity on complex domains (e.g., image, structural data, and sequential data). The underlying idea is to learn domain invariant representations on a latent space that can bridge the gap between source and target domains. Several theoretical studies have established insightful understanding and the benefit of learning domain invariant features; however, they are usually limited to the case where there is no label shift, hence hindering its applicability. In this paper, we propose and study a new challenging setting that allows us to use a Wasserstein distance (WS) to not only quantify the data shift but also to define the label shift directly. We further develop a theory to demonstrate that minimizing the WS of the data shift leads to closing the gap between the source and target data distributions on the latent space (e.g., an intermediate layer of a deep net), while still being able to quantify the label shift with respect to this latent space. Interestingly, our theory can consequently explain certain drawbacks of learning domain invariant features on the latent space. Finally, grounded on the results and guidance of our developed theory, we propose the Label Matching Deep Domain Adaptation (LAMDA) approach that outperforms baselines on real-world datasets for DA problems. | Trung Le, Tuan Nguyen, Nhat Ho, Hung Bui, Dinh Phung | null | null | 2,021 | icml |
PEBBLE: Feedback-Efficient Interactive Reinforcement Learning via Relabeling Experience and Unsupervised Pre-training | null | Conveying complex objectives to reinforcement learning (RL) agents can often be difficult, involving meticulous design of reward functions that are sufficiently informative yet easy enough to provide. Human-in-the-loop RL methods allow practitioners to instead interactively teach agents through tailored feedback; however, such approaches have been challenging to scale since human feedback is very expensive. In this work, we aim to make this process more sample- and feedback-efficient. We present an off-policy, interactive RL algorithm that capitalizes on the strengths of both feedback and off-policy learning. Specifically, we learn a reward model by actively querying a teacher’s preferences between two clips of behavior and use it to train an agent. To enable off-policy learning, we relabel all the agent’s past experience when its reward model changes. We additionally show that pre-training our agents with unsupervised exploration substantially increases the mileage of its queries. We demonstrate that our approach is capable of learning tasks of higher complexity than previously considered by human-in-the-loop methods, including a variety of locomotion and robotic manipulation skills. We also show that our method is able to utilize real-time human feedback to effectively prevent reward exploitation and learn new behaviors that are difficult to specify with standard reward functions. | Kimin Lee, Laura M Smith, Pieter Abbeel | null | null | 2,021 | icml |
Scalable Evaluation of Multi-Agent Reinforcement Learning with Melting Pot | null | Existing evaluation suites for multi-agent reinforcement learning (MARL) do not assess generalization to novel situations as their primary objective (unlike supervised learning benchmarks). Our contribution, Melting Pot, is a MARL evaluation suite that fills this gap and uses reinforcement learning to reduce the human labor required to create novel test scenarios. This works because one agent’s behavior constitutes (part of) another agent’s environment. To demonstrate scalability, we have created over 80 unique test scenarios covering a broad range of research topics such as social dilemmas, reciprocity, resource sharing, and task partitioning. We apply these test scenarios to standard MARL training algorithms, and demonstrate how Melting Pot reveals weaknesses not apparent from training performance alone. | Joel Z Leibo, Edgar A Dueñez-Guzman, Alexander Vezhnevets, John P Agapiou, Peter Sunehag, Raphael Koster, Jayd Matyas, Charlie Beattie, Igor Mordatch, Thore Graepel | null | null | 2,021 | icml |
Stability and Generalization of Stochastic Gradient Methods for Minimax Problems | null | Many machine learning problems can be formulated as minimax problems such as Generative Adversarial Networks (GANs), AUC maximization and robust estimation, to mention but a few. A substantial amount of studies are devoted to studying the convergence behavior of their stochastic gradient-type algorithms. In contrast, there is relatively little work on understanding their generalization, i.e., how the learning models built from training examples would behave on test examples. In this paper, we provide a comprehensive generalization analysis of stochastic gradient methods for minimax problems under both convex-concave and nonconvex-nonconcave cases through the lens of algorithmic stability. We establish a quantitative connection between stability and several generalization measures both in expectation and with high probability. For the convex-concave setting, our stability analysis shows that stochastic gradient descent ascent attains optimal generalization bounds for both smooth and nonsmooth minimax problems. We also establish generalization bounds for both weakly-convex-weakly-concave and gradient-dominated problems. We report preliminary experimental results to verify our theory. | Yunwen Lei, Zhenhuan Yang, Tianbao Yang, Yiming Ying | null | null | 2,021 | icml |
Discovering symbolic policies with deep reinforcement learning | null | Deep reinforcement learning (DRL) has proven successful for many difficult control problems by learning policies represented by neural networks. However, the complexity of neural network-based policies{—}involving thousands of composed non-linear operators{—}can render them problematic to understand, trust, and deploy. In contrast, simple policies comprising short symbolic expressions can facilitate human understanding, while also being transparent and exhibiting predictable behavior. To this end, we propose deep symbolic policy, a novel approach to directly search the space of symbolic policies. We use an autoregressive recurrent neural network to generate control policies represented by tractable mathematical expressions, employing a risk-seeking policy gradient to maximize performance of the generated policies. To scale to environments with multi-dimensional action spaces, we propose an "anchoring" algorithm that distills pre-trained neural network-based policies into fully symbolic policies, one action dimension at a time. We also introduce two novel methods to improve exploration in DRL-based combinatorial optimization, building on ideas of entropy regularization and distribution initialization. Despite their dramatically reduced complexity, we demonstrate that discovered symbolic policies outperform seven state-of-the-art DRL algorithms in terms of average rank and average normalized episodic reward across eight benchmark environments. | Mikel Landajuela, Brenden K Petersen, Sookyung Kim, Claudio P Santiago, Ruben Glatt, Nathan Mundhenk, Jacob F Pettit, Daniel Faissol | null | null | 2,021 | icml |
A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samples | null | We propose an iterative algorithm for low-rank matrix completion with that can be interpreted as an iteratively reweighted least squares (IRLS) algorithm, a saddle-escaping smoothing Newton method or a variable metric proximal gradient method applied to a non-convex rank surrogate. It combines the favorable data-efficiency of previous IRLS approaches with an improved scalability by several orders of magnitude. We establish the first local convergence guarantee from a minimal number of samples for that class of algorithms, showing that the method attains a local quadratic convergence rate. Furthermore, we show that the linear systems to be solved are well-conditioned even for very ill-conditioned ground truth matrices. We provide extensive experiments, indicating that unlike many state-of-the-art approaches, our method is able to complete very ill-conditioned matrices with a condition number of up to $10^{10}$ from few samples, while being competitive in its scalability. | Christian Kümmerle, Claudio M. Verdun | null | null | 2,021 | icml |
Run-Sort-ReRun: Escaping Batch Size Limitations in Sliced Wasserstein Generative Models | null | When training an implicit generative model, ideally one would like the generator to reproduce all the different modes and subtleties of the target distribution. Naturally, when comparing two empirical distributions, the larger the sample population, the more these statistical nuances can be captured. However, existing objective functions are computationally constrained in the amount of samples they can consider by the memory required to process a batch of samples. In this paper, we build upon recent progress in sliced Wasserstein distances, a family of differentiable metrics for distribution discrepancy based on the Optimal Transport paradigm. We introduce a procedure to train these distances with virtually any batch size, allowing the discrepancy measure to capture richer statistics and better approximating the distance between the underlying continuous distributions. As an example, we demonstrate the matching of the distribution of Inception features with batches of tens of thousands of samples, achieving FID scores that outperform state-of-the-art implicit generative models. | Jose Lezama, Wei Chen, Qiang Qiu | null | null | 2,021 | icml |
Theory of Spectral Method for Union of Subspaces-Based Random Geometry Graph | null | Spectral method is a commonly used scheme to cluster data points lying close to Union of Subspaces, a task known as Subspace Clustering. The typical usage is to construct a Random Geometry Graph first and then apply spectral method to the graph to obtain clustering result. The latter step has been coined the name Spectral Clustering. As far as we know, in spite of the significance of both steps in spectral-method-based Subspace Clustering, all existing theoretical results focus on the first step of constructing the graph, but ignore the final step to correct false connections through spectral clustering. This paper establishes a theory to show the power of this method for the first time, in which we demonstrate the mechanism of spectral clustering by analyzing a simplified algorithm under the widely used semi-random model. Based on this theory, we prove the efficiency of Subspace Clustering in fairly broad conditions. The insights and analysis techniques developed in this paper might also have implications for other random graph problems. | Gen Li, Yuantao Gu | null | null | 2,021 | icml |
MURAL: Meta-Learning Uncertainty-Aware Rewards for Outcome-Driven Reinforcement Learning | null | Exploration in reinforcement learning is, in general, a challenging problem. A common technique to make learning easier is providing demonstrations from a human supervisor, but such demonstrations can be expensive and time-consuming to acquire. In this work, we study a more tractable class of reinforcement learning problems defined simply by examples of successful outcome states, which can be much easier to provide while still making the exploration problem more tractable. In this problem setting, the reward function can be obtained automatically by training a classifier to categorize states as successful or not. However, as we will show, this requires the classifier to make uncertainty-aware predictions that are very difficult using standard techniques for training deep networks. To address this, we propose a novel mechanism for obtaining calibrated uncertainty based on an amortized technique for computing the normalized maximum likelihood (NML) distribution, leveraging tools from meta-learning to make this distribution tractable. We show that the resulting algorithm has a number of intriguing connections to both count-based exploration methods and prior algorithms for learning reward functions, while also providing more effective guidance towards the goal. We demonstrate that our algorithm solves a number of challenging navigation and robotic manipulation tasks which prove difficult or impossible for prior methods. | Kevin Li, Abhishek Gupta, Ashwin Reddy, Vitchyr H Pong, Aurick Zhou, Justin Yu, Sergey Levine | null | null | 2,021 | icml |
A Free Lunch From ANN: Towards Efficient, Accurate Spiking Neural Networks Calibration | null | Spiking Neural Network (SNN) has been recognized as one of the next generation of neural networks. Conventionally, SNN can be converted from a pre-trained ANN by only replacing the ReLU activation to spike activation while keeping the parameters intact. Perhaps surprisingly, in this work we show that a proper way to calibrate the parameters during the conversion of ANN to SNN can bring significant improvements. We introduce SNN Calibration, a cheap but extraordinarily effective method by leveraging the knowledge within a pre-trained Artificial Neural Network (ANN). Starting by analyzing the conversion error and its propagation through layers theoretically, we propose the calibration algorithm that can correct the error layer-by-layer. The calibration only takes a handful number of training data and several minutes to finish. Moreover, our calibration algorithm can produce SNN with state-of-the-art architecture on the large-scale ImageNet dataset, including MobileNet and RegNet. Extensive experiments demonstrate the effectiveness and efficiency of our algorithm. For example, our advanced pipeline can increase up to 69% top-1 accuracy when converting MobileNet on ImageNet compared to baselines. Codes are released at https://github.com/yhhhli/SNN_Calibration. | Yuhang Li, Shikuang Deng, Xin Dong, Ruihao Gong, Shi Gu | null | null | 2,021 | icml |
Approximate Group Fairness for Clustering | null | We incorporate group fairness into the algorithmic centroid clustering problem, where $k$ centers are to be located to serve $n$ agents distributed in a metric space. We refine the notion of proportional fairness proposed in [Chen et al., ICML 2019] as {\em core fairness}. A $k$-clustering is in the core if no coalition containing at least $n/k$ agents can strictly decrease their total distance by deviating to a new center together. Our solution concept is motivated by the situation where agents are able to coordinate and utilities are transferable. A string of existence, hardness and approximability results is provided. Particularly, we propose two dimensions to relax core requirements: one is on the degree of distance improvement, and the other is on the size of deviating coalition. For both relaxations and their combination, we study the extent to which relaxed core fairness can be satisfied in metric spaces including line, tree and general metric space, and design approximation algorithms accordingly. We also conduct experiments on synthetic and real-world data to examine the performance of our algorithms. | Bo Li, Lijun Li, Ankang Sun, Chenhao Wang, Yingfan Wang | null | null | 2,021 | icml |
Tightening the Dependence on Horizon in the Sample Complexity of Q-Learning | null | Q-learning, which seeks to learn the optimal Q-function of a Markov decision process (MDP) in a model-free fashion, lies at the heart of reinforcement learning. Focusing on the synchronous setting (such that independent samples for all state-action pairs are queried via a generative model in each iteration), substantial progress has been made recently towards understanding the sample efficiency of Q-learning. To yield an entrywise $\varepsilon$-accurate estimate of the optimal Q-function, state-of-the-art theory requires at least an order of $\frac{|S||A|}{(1-\gamma)^5\varepsilon^{2}}$ samples in the infinite-horizon $\gamma$-discounted setting. In this work, we sharpen the sample complexity of synchronous Q-learning to the order of $\frac{|S||A|}{(1-\gamma)^4\varepsilon^2}$ (up to some logarithmic factor) for any $0<\varepsilon <1$, leading to an order-wise improvement in $\frac{1}{1-\gamma}$. Analogous results are derived for finite-horizon MDPs as well. Notably, our sample complexity analysis unveils the effectiveness of vanilla Q-learning, which matches that of speedy Q-learning without requiring extra computation and storage. Our result is obtained by identifying novel error decompositions and recursion relations, which might shed light on how to study other variants of Q-learning. | Gen Li, Changxiao Cai, Yuxin Chen, Yuantao Gu, Yuting Wei, Yuejie Chi | null | null | 2,021 | icml |
Provably End-to-end Label-noise Learning without Anchor Points | null | In label-noise learning, the transition matrix plays a key role in building statistically consistent classifiers. Existing consistent estimators for the transition matrix have been developed by exploiting anchor points. However, the anchor-point assumption is not always satisfied in real scenarios. In this paper, we propose an end-to-end framework for solving label-noise learning without anchor points, in which we simultaneously optimize two objectives: the cross entropy loss between the noisy label and the predicted probability by the neural network, and the volume of the simplex formed by the columns of the transition matrix. Our proposed framework can identify the transition matrix if the clean class-posterior probabilities are sufficiently scattered. This is by far the mildest assumption under which the transition matrix is provably identifiable and the learned classifier is statistically consistent. Experimental results on benchmark datasets demonstrate the effectiveness and robustness of the proposed method. | Xuefeng Li, Tongliang Liu, Bo Han, Gang Niu, Masashi Sugiyama | null | null | 2,021 | icml |
BASE Layers: Simplifying Training of Large, Sparse Models | null | We introduce a new balanced assignment of experts (BASE) layer for large language models that greatly simplifies existing high capacity sparse layers. Sparse layers can dramatically improve the efficiency of training and inference by routing each token to specialized expert modules that contain only a small fraction of the model parameters. However, it can be difficult to learn balanced routing functions that make full use of the available experts; existing approaches typically use routing heuristics or auxiliary expert-balancing loss functions. In contrast, we formulate token-to-expert allocation as a linear assignment problem, allowing an optimal assignment in which each expert receives an equal number of tokens. This optimal assignment scheme improves efficiency by guaranteeing balanced compute loads, and also simplifies training by not requiring any new hyperparameters or auxiliary losses. Code is publicly released. | Mike Lewis, Shruti Bhosale, Tim Dettmers, Naman Goyal, Luke Zettlemoyer | null | null | 2,021 | icml |
Sharper Generalization Bounds for Clustering | null | Existing generalization analysis of clustering mainly focuses on specific instantiations, such as (kernel) $k$-means, and a unified framework for studying clustering performance is still lacking. Besides, the existing excess clustering risk bounds are mostly of order $\mathcal{O}(K/\sqrt{n})$ provided that the underlying distribution has bounded support, where $n$ is the sample size and $K$ is the cluster numbers, or of order $\mathcal{O}(K^2/n)$ under strong assumptions on the underlying distribution, where these assumptions are hard to be verified in general. In this paper, we propose a unified clustering learning framework and investigate its excess risk bounds, obtaining state-of-the-art upper bounds under mild assumptions. Specifically, we derive sharper bounds of order $\mathcal{O}(K^2/n)$ under mild assumptions on the covering number of the hypothesis spaces, where these assumptions are easy to be verified. Moreover, for the hard clustering scheme, such as (kernel) $k$-means, if just assume the hypothesis functions to be bounded, we improve the upper bounds from the order $\mathcal{O}(K/\sqrt{n})$ to $\mathcal{O}(\sqrt{K}/\sqrt{n})$. Furthermore, state-of-the-art bounds of faster order $\mathcal{O}(K/n)$ are obtained with the covering number assumptions. | Shaojie Li, Yong Liu | null | null | 2,021 | icml |
The Symmetry between Arms and Knapsacks: A Primal-Dual Approach for Bandits with Knapsacks | null | In this paper, we study the bandits with knapsacks (BwK) problem and develop a primal-dual based algorithm that achieves a problem-dependent logarithmic regret bound. The BwK problem extends the multi-arm bandit (MAB) problem to model the resource consumption, and the existing BwK literature has been mainly focused on deriving asymptotically optimal distribution-free regret bounds. We first study the primal and dual linear programs underlying the BwK problem. From this primal-dual perspective, we discover symmetry between arms and knapsacks, and then propose a new notion of suboptimality measure for the BwK problem. The suboptimality measure highlights the important role of knapsacks in determining algorithm regret and inspires the design of our two-phase algorithm. In the first phase, the algorithm identifies the optimal arms and the binding knapsacks, and in the second phase, it exhausts the binding knapsacks via playing the optimal arms through an adaptive procedure. Our regret upper bound involves the proposed suboptimality measure and it has a logarithmic dependence on length of horizon $T$ and a polynomial dependence on $m$ (the numbers of arms) and $d$ (the number of knapsacks). To the best of our knowledge, this is the first problem-dependent logarithmic regret bound for solving the general BwK problem. | Xiaocheng Li, Chunlin Sun, Yinyu Ye | null | null | 2,021 | icml |
Mixed Cross Entropy Loss for Neural Machine Translation | null | In neural machine translation, Cross Entropy loss (CE) is the standard loss function in two training methods of auto-regressive models, i.e., teacher forcing and scheduled sampling. In this paper, we propose mixed Cross Entropy loss (mixed CE) as a substitute for CE in both training approaches. In teacher forcing, the model trained with CE regards the translation problem as a one-to-one mapping process, while in mixed CE this process can be relaxed to one-to-many. In scheduled sampling, we show that mixed CE has the potential to encourage the training and testing behaviours to be similar to each other, more effectively mitigating the exposure bias problem. We demonstrate the superiority of mixed CE over CE on several machine translation datasets, WMT’16 Ro-En, WMT’16 Ru-En, and WMT’14 En-De in both teacher forcing and scheduled sampling setups. Furthermore, in WMT’14 En-De, we also find mixed CE consistently outperforms CE on a multi-reference set as well as a challenging paraphrased reference set. We also found the model trained with mixed CE is able to provide a better probability distribution defined over the translation output space. Our code is available at https://github.com/haorannlp/mix. | Haoran Li, Wei Lu | null | null | 2,021 | icml |
PAGE: A Simple and Optimal Probabilistic Gradient Estimator for Nonconvex Optimization | null | In this paper, we propose a novel stochastic gradient estimator—ProbAbilistic Gradient Estimator (PAGE)—for nonconvex optimization. PAGE is easy to implement as it is designed via a small adjustment to vanilla SGD: in each iteration, PAGE uses the vanilla minibatch SGD update with probability $p_t$ or reuses the previous gradient with a small adjustment, at a much lower computational cost, with probability $1-p_t$. We give a simple formula for the optimal choice of $p_t$. Moreover, we prove the first tight lower bound $\Omega(n+\frac{\sqrt{n}}{\epsilon^2})$ for nonconvex finite-sum problems, which also leads to a tight lower bound $\Omega(b+\frac{\sqrt{b}}{\epsilon^2})$ for nonconvex online problems, where $b:= \min\{\frac{\sigma^2}{\epsilon^2}, n\}$. Then, we show that PAGE obtains the optimal convergence results $O(n+\frac{\sqrt{n}}{\epsilon^2})$ (finite-sum) and $O(b+\frac{\sqrt{b}}{\epsilon^2})$ (online) matching our lower bounds for both nonconvex finite-sum and online problems. Besides, we also show that for nonconvex functions satisfying the Polyak-Ł{ojasiewicz} (PL) condition, PAGE can automatically switch to a faster linear convergence rate $O(\cdot\log \frac{1}{\epsilon})$. Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch showing that PAGE not only converges much faster than SGD in training but also achieves the higher test accuracy, validating the optimal theoretical results and confirming the practical superiority of PAGE. | Zhize Li, Hongyan Bao, Xiangliang Zhang, Peter Richtarik | null | null | 2,021 | icml |
A Novel Method to Solve Neural Knapsack Problems | null | 0-1 knapsack is of fundamental importance across many fields. In this paper, we present a game-theoretic method to solve 0-1 knapsack problems (KPs) where the number of items (products) is large and the values of items are not predetermined but decided by an external value assignment function (e.g., a neural network in our case) during the optimization process. While existing papers are interested in predicting solutions with neural networks for classical KPs whose objective functions are mostly linear functions, we are interested in solving KPs whose objective functions are neural networks. In other words, we choose a subset of items that maximize the sum of the values predicted by neural networks. Its key challenge is how to optimize the neural network-based non-linear KP objective with a budget constraint. Our solution is inspired by game-theoretic approaches in deep learning, e.g., generative adversarial networks. After formally defining our two-player game, we develop an adaptive gradient ascent method to solve it. In our experiments, our method successfully solves two neural network-based non-linear KPs and conventional linear KPs with 1 million items. | Duanshun Li, Jing Liu, Dongeun Lee, Ali Seyedmazloom, Giridhar Kaushik, Kookjin Lee, Noseong Park | null | null | 2,021 | icml |
Online Unrelated Machine Load Balancing with Predictions Revisited | null | We study the online load balancing problem with machine learned predictions, and give results that improve upon and extend those in a recent paper by Lattanzi et al. (2020). First, we design deterministic and randomized online rounding algorithms for the problem in the unrelated machine setting, with $O(\frac{\log m}{\log \log m})$- and $O(\frac{\log \log m}{\log \log \log m})$-competitive ratios. They respectively improve upon the previous ratios of $O(\log m)$ and $O(\log^3\log m)$, and match the lower bounds given by Lattanzi et al. Second, we extend their prediction scheme from the identical machine restricted assignment setting to the unrelated machine setting. With the knowledge of two vectors over machines, a dual vector and a weight vector, we can construct a good fractional assignment online, that can be passed to an online rounding algorithm. Finally, we consider the learning model introduced by Lavastida et al. (2020), and show that under the model, the two vectors can be learned efficiently with a few samples of instances. | Shi Li, Jiayi Xian | null | null | 2,021 | icml |
A Second look at Exponential and Cosine Step Sizes: Simplicity, Adaptivity, and Performance | null | Stochastic Gradient Descent (SGD) is a popular tool in training large-scale machine learning models. Its performance, however, is highly variable, depending crucially on the choice of the step sizes. Accordingly, a variety of strategies for tuning the step sizes have been proposed, ranging from coordinate-wise approaches (a.k.a. “adaptive” step sizes) to sophisticated heuristics to change the step size in each iteration. In this paper, we study two step size schedules whose power has been repeatedly confirmed in practice: the exponential and the cosine step sizes. For the first time, we provide theoretical support for them proving convergence rates for smooth non-convex functions, with and without the Polyak-Ł{}ojasiewicz (PL) condition. Moreover, we show the surprising property that these two strategies are \emph{adaptive} to the noise level in the stochastic gradients of PL functions. That is, contrary to polynomial step sizes, they achieve almost optimal performance without needing to know the noise level nor tuning their hyperparameters based on it. Finally, we conduct a fair and comprehensive empirical evaluation of real-world datasets with deep learning architectures. Results show that, even if only requiring at most two hyperparameters to tune, these two strategies best or match the performance of various finely-tuned state-of-the-art strategies. | Xiaoyu Li, Zhenxun Zhuang, Francesco Orabona | null | null | 2,021 | icml |
Asymptotic Normality and Confidence Intervals for Prediction Risk of the Min-Norm Least Squares Estimator | null | This paper quantifies the uncertainty of prediction risk for the min-norm least squares estimator in high-dimensional linear regression models. We establish the asymptotic normality of prediction risk when both the sample size and the number of features tend to infinity. Based on the newly established central limit theorems(CLTs), we derive the confidence intervals of the prediction risk under various scenarios. Our results demonstrate the sample-wise non-monotonicity of the prediction risk and confirm “more data hurt" phenomenon. Furthermore, the width of confidence intervals indicates that over-parameterization would enlarge the randomness of prediction performance. | Zeng Li, Chuanlong Xie, Qinwen Wang | null | null | 2,021 | icml |
Uncovering the Connections Between Adversarial Transferability and Knowledge Transferability | null | Knowledge transferability, or transfer learning, has been widely adopted to allow a pre-trained model in the source domain to be effectively adapted to downstream tasks in the target domain. It is thus important to explore and understand the factors affecting knowledge transferability. In this paper, as the first work, we analyze and demonstrate the connections between knowledge transferability and another important phenomenon–adversarial transferability, \emph{i.e.}, adversarial examples generated against one model can be transferred to attack other models. Our theoretical studies show that adversarial transferability indicates knowledge transferability, and vice versa. Moreover, based on the theoretical insights, we propose two practical adversarial transferability metrics to characterize this process, serving as bidirectional indicators between adversarial and knowledge transferability. We conduct extensive experiments for different scenarios on diverse datasets, showing a positive correlation between adversarial transferability and knowledge transferability. Our findings will shed light on future research about effective knowledge transfer learning and adversarial transferability analyses. | Kaizhao Liang, Jacky Y Zhang, Boxin Wang, Zhuolin Yang, Sanmi Koyejo, Bo Li | null | null | 2,021 | icml |
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