Daily Papers

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees, while achieving competitive empirical performance.

We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a general framework for first-order optimization of these processes, that performs jointly, in a single loop, optimization and sampling steps. This approach is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the point of view of sampling as optimization over the space of probability distributions. We provide theoretical guarantees on the performance of our method, as well as experimental results demonstrating its effectiveness in real-world settings.

Reinforcement learning from human feedback (RLHF) is a standard approach for fine-tuning large language models to follow instructions. As part of this process, learned reward models are used to approximately model human preferences. However, as imperfect representations of the "true" reward, these learned reward models are susceptible to overoptimization. Gao et al. (2023) studied this phenomenon in a synthetic human feedback setup with a significantly larger "gold" reward model acting as the true reward (instead of humans) and showed that overoptimization remains a persistent problem regardless of the size of the proxy reward model and training data used. Using a similar setup, we conduct a systematic study to evaluate the efficacy of using ensemble-based conservative optimization objectives, specifically worst-case optimization (WCO) and uncertainty-weighted optimization (UWO), for mitigating reward model overoptimization when using two optimization methods: (a) best-of-n sampling (BoN) (b) proximal policy optimization (PPO). We additionally extend the setup of Gao et al. (2023) to include 25% label noise to better mirror real-world conditions. Both with and without label noise, we find that conservative optimization practically eliminates overoptimization and improves performance by up to 70% for BoN sampling. For PPO, ensemble-based conservative optimization always reduces overoptimization and outperforms single reward model optimization. Moreover, combining it with a small KL penalty successfully prevents overoptimization at no performance cost. Overall, our results demonstrate that ensemble-based conservative optimization can effectively counter overoptimization.

Ecological management and decision-making typically focus on uncertainty about the future, but surprisingly little is known about how to account for uncertainty of the present: that is, the realities of having only partial or imperfect measurements. Our primary paradigms for handling decisions under uncertainty -- the precautionary principle and optimal control -- have so far given contradictory results. This paradox is best illustrated in the example of fisheries management, where many ideas that guide thinking about ecological decision making were first developed. We find that simplistic optimal control approaches have repeatedly concluded that a manager should increase catch quotas when faced with greater uncertainty about the fish biomass. Current best practices take a more precautionary approach, decreasing catch quotas by a fixed amount to account for uncertainty. Using comparisons to both simulated and historical catch data, we find that neither approach is sufficient to avoid stock collapses under moderate observational uncertainty. Using partially observed Markov decision process (POMDP) methods, we demonstrate how this paradox arises from flaws in the standard theory, which contributes to over-exploitation of fisheries and increased probability of economic and ecological collapse. In contrast, we find POMDP-based management avoids such over-exploitation while also generating higher economic value. These results have significant implications for how we handle uncertainty in both fisheries and ecological management more generally.

Diffusion models have shown strong competitiveness in offline reinforcement learning tasks by formulating decision-making as sequential generation. However, the practicality of these methods is limited due to the lengthy inference processes they require. In this paper, we address this problem by decomposing the sampling process of diffusion models into two decoupled subprocesses: 1) generating a feasible trajectory, which is a time-consuming process, and 2) optimizing the trajectory. With this decomposition approach, we are able to partially separate efficiency and quality factors, enabling us to simultaneously gain efficiency advantages and ensure quality assurance. We propose the Trajectory Diffuser, which utilizes a faster autoregressive model to handle the generation of feasible trajectories while retaining the trajectory optimization process of diffusion models. This allows us to achieve more efficient planning without sacrificing capability. To evaluate the effectiveness and efficiency of the Trajectory Diffuser, we conduct experiments on the D4RL benchmarks. The results demonstrate that our method achieves it 3-it 10 times faster inference speed compared to previous sequence modeling methods, while also outperforming them in terms of overall performance. https://github.com/RenMing-Huang/TrajectoryDiffuser Keywords: Reinforcement Learning and Efficient Planning and Diffusion Model

In this paper, we study the predict-then-optimize problem where the output of a machine learning prediction task is used as the input of some downstream optimization problem, say, the objective coefficient vector of a linear program. The problem is also known as predictive analytics or contextual linear programming. The existing approaches largely suffer from either (i) optimization intractability (a non-convex objective function)/statistical inefficiency (a suboptimal generalization bound) or (ii) requiring strong condition(s) such as no constraint or loss calibration. We develop a new approach to the problem called maximum optimality margin which designs the machine learning loss function by the optimality condition of the downstream optimization. The max-margin formulation enjoys both computational efficiency and good theoretical properties for the learning procedure. More importantly, our new approach only needs the observations of the optimal solution in the training data rather than the objective function, which makes it a new and natural approach to the inverse linear programming problem under both contextual and context-free settings; we also analyze the proposed method under both offline and online settings, and demonstrate its performance using numerical experiments.

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization".

Combinatorial optimization (CO) is naturally discrete, making machine learning based on differentiable optimization inapplicable. Karalias & Loukas (2020) adapted the probabilistic method to incorporate CO into differentiable optimization. Their work ignited the research on unsupervised learning for CO, composed of two main components: probabilistic objectives and derandomization. However, each component confronts unique challenges. First, deriving objectives under various conditions (e.g., cardinality constraints and minimum) is nontrivial. Second, the derandomization process is underexplored, and the existing derandomization methods are either random sampling or naive rounding. In this work, we aim to tackle prevalent (i.e., commonly involved) conditions in unsupervised CO. First, we concretize the targets for objective construction and derandomization with theoretical justification. Then, for various conditions commonly involved in different CO problems, we derive nontrivial objectives and derandomization to meet the targets. Finally, we apply the derivations to various CO problems. Via extensive experiments on synthetic and real-world graphs, we validate the correctness of our derivations and show our empirical superiority w.r.t. both optimization quality and speed.