NeurIPS 2023 论文列表

This paper presents a unified approach for maximizing continuous DR-submodular functions that encompasses a range of settings and oracle access types. Our approach includes a Frank-Wolfe type offline algorithm for both monotone and non-monotone functions, with different restrictions on the general convex set. We consider settings where the oracle provides access to either the gradient of the function or only the function value, and where the oracle access is either deterministic or stochastic. We determine the number of required oracle accesses in all cases. Our approach gives new/improved results for nine out of the sixteen considered cases, avoids computationally expensive projections in three cases, with the proposed framework matching performance of state-of-the-art approaches in the remaining four cases. Notably, our approach for the stochastic function value-based oracle enables the first regret bounds with bandit feedback for stochastic DR-submodular functions.

This work presents ReSync, a Riemannian subgradient-based algorithm for solving the robust rotation synchronization problem, which arises in various engineering applications. ReSync solves a least-unsquared minimization formulation over the rotation group, which is nonsmooth and nonconvex, and aims at recovering the underlying rotations directly. We provide strong theoretical guarantees for ReSync under the random corruption setting. Specifically, we first show that the initialization procedure of ReSync yields a proper initial point that lies in a local region around the ground-truth rotations. We next establish the weak sharpness property of the aforementioned formulation and then utilize this property to derive the local linear convergence of ReSync to the ground-truth rotations. By combining these guarantees, we conclude that ReSync converges linearly to the ground-truth rotations under appropriate conditions. Experiment results demonstrate the effectiveness of ReSync.

Despite its flexibility to learn diverse inductive biases in machine learning programs, meta learning (i.e.,\ learning to learn) has long been recognized to suffer from poor scalability due to its tremendous compute/memory costs, training instability, and a lack of efficient distributed training support. In this work, we focus on making scalable meta learning practical by introducing SAMA, which combines advances in both implicit differentiation algorithms and systems. Specifically, SAMA is designed to flexibly support a broad range of adaptive optimizers in the base level of meta learning programs, while reducing computational burden by avoiding explicit computation of second-order gradient information, and exploiting efficient distributed training techniques implemented for first-order gradients. Evaluated on multiple large-scale meta learning benchmarks, SAMA showcases up to 1.7/4.8x increase in throughput and 2.0/3.8x decrease in memory consumption respectively on single-/multi-GPU setups compared to other baseline meta learning algorithms. Furthermore, we show that SAMA-based data optimization leads to consistent improvements in text classification accuracy with BERT and RoBERTa large language models, and achieves state-of-the-art results in both small- and large-scale data pruning on image classification tasks, demonstrating the practical applicability of scalable meta learning across language and vision domains.

We study the convergence behavior of the celebrated temporal-difference (TD) learning algorithm. By looking at the algorithm through the lens of optimization, we first argue that TD can be viewed as an iterative optimization algorithm where the function to be minimized changes per iteration. By carefully investigating the divergence displayed by TD on a classical counter example, we identify two forces that determine the convergent or divergent behavior of the algorithm. We next formalize our discovery in the linear TD setting with quadratic loss and prove that convergence of TD hinges on the interplay between these two forces. We extend this optimization perspective to prove convergence of TD in a much broader setting than just linear approximation and squared loss. Our results provide a theoretical explanation for the successful application of TD in reinforcement learning.

Bilevel optimization has become a powerful tool in a wide variety of machine learning problems. However, the current nonconvex bilevel optimization considers an offline dataset and static functions, which may not work well in emerging online applications with streaming data and time-varying functions. In this work, we study online bilevel optimization (OBO) where the functions can be time-varying and the agent continuously updates the decisions with online streaming data. To deal with the function variations and the unavailability of the true hypergradients in OBO, we propose a single-loop online bilevel optimizer with window averaging (SOBOW), which updates the outer-level decision based on a window average of the most recent hypergradient estimations stored in the memory. Compared to existing algorithms, SOBOW is computationally efficient and does not need to know previous functions. To handle the unique technical difficulties rooted in single-loop update and function variations for OBO, we develop a novel analytical technique that disentangles the complex couplings between decision variables, and carefully controls the hypergradient estimation error. We show that SOBOW can achieve a sublinear bilevel local regret under mild conditions. Extensive experiments across multiple domains corroborate the effectiveness of SOBOW.

The aim of this paper is to improve the understanding of the optimization landscape for policy optimization problems in reinforcement learning. Specifically, we show that the superlevel set of the objective function with respect to the policy parameter is always a connected set both in the tabular setting and under policies represented by a class of neural networks. In addition, we show that the optimization objective as a function of the policy parameter and reward satisfies a stronger “equiconnectedness” property. To our best knowledge, these are novel and previously unknown discoveries. We present an application of the connectedness of these superlevel sets to the derivation of minimax theorems for robust reinforcement learning. We show that any minimax optimization program which is convex on one side and is equiconnected on the other side observes the minimax equality (i.e. has a Nash equilibrium). We find that this exact structure is exhibited by an interesting class of robust reinforcement learning problems under an adversarial reward attack, and the validity of its minimax equality immediately follows. This is the first time such a result is established in the literature.

Carefully designed activation functions can improve the performance of neural networks in many machine learning tasks. However, it is difficult for humans to construct optimal activation functions, and current activation function search algorithms are prohibitively expensive. This paper aims to improve the state of the art through three steps: First, the benchmark datasets Act-Bench-CNN, Act-Bench-ResNet, and Act-Bench-ViT were created by training convolutional, residual, and vision transformer architectures from scratch with 2,913 systematically generated activation functions. Second, a characterization of the benchmark space was developed, leading to a new surrogate-based method for optimization. More specifically, the spectrum of the Fisher information matrix associated with the model's predictive distribution at initialization and the activation function's output distribution were found to be highly predictive of performance. Third, the surrogate was used to discover improved activation functions in several real-world tasks, with a surprising finding: a sigmoidal design that outperformed all other activation functions was discovered, challenging the status quo of always using rectifier nonlinearities in deep learning. Each of these steps is a contribution in its own right; together they serve as a practical and theoretical foundation for further research on activation function optimization.

Graph learning from signals is a core task in graph signal processing (GSP). A significant subclass of graph signals called the stationary graph signals that broadens the concept of stationarity of data defined on regular domains to signals on graphs is gaining increasing popularity in the GSP community. The most commonly used model to learn graphs from these stationary signals is SpecT, which forms the foundation for nearly all the subsequent, more advanced models. Despite its strengths, the practical formulation of the model, known as rSpecT, has been identified to be susceptible to the choice of hyperparameters. More critically, it may suffer from infeasibility as an optimization problem. In this paper, we introduce the first condition that ensures the infeasibility of rSpecT and design a novel model called LogSpecT, along with its practical formulation rLogSpecT to overcome this issue. Contrary to rSpecT, our novel practical model rLogSpecT is always feasible. Furthermore, we provide recovery guarantees of rLogSpecT from modern optimization tools related to epi-convergence, which could be of independent interest and significant for various learning problems. To demonstrate the practical advantages of rLogSpecT, a highly efficient algorithm based on the linearized alternating direction method of multipliers (L-ADMM) that allows closed-form solutions for each subproblem is proposed with convergence guarantees. Extensive numerical results on both synthetic and real networks not only corroborate the stability of our proposed methods, but also highlight their comparable and even superior performance than existing models.

The design automation of analog circuits poses significant challenges in terms of the large design space, complex interdependencies between circuit specifications, and resource-intensive simulations. To address these challenges, this paper presents an innovative framework called the Graph of Circuits Explorer (GCX). Leveraging graph structure learning along with graph neural networks, GCX enables the creation of a surrogate model that facilitates efficient exploration of the optimal design space within a semi-supervised learning framework which reduces the need for large labelled datasets. The proposed approach comprises three key stages. First, we learn the geometric representation of circuits and enrich it with technology information to create a comprehensive feature vector. Subsequently, integrating feature-based graph learning with few-shot and zero-shot learning enhances the generalizability in predictions for unseen circuits. Finally, we introduce two algorithms namely, EASCO and ASTROG which upon integration with GCX optimize the available samples to yield the optimal circuit configuration meeting the designer's criteria. The effectiveness of the proposed approach is demonstrated through simulated performance evaluation of various circuits, using derived parameters in 180nm CMOS technology. Furthermore, the generalizability of the approach is extended to higher-order topologies and different technology nodes such as 65nm and 45nm CMOS process nodes.

A long line of works characterizes the sample complexity of regret minimization in sequential decision-making by min-max programs. In the corresponding saddle-point game, the min-player optimizes the sampling distribution against an adversarial max-player that chooses confusing models leading to large regret. The most recent instantiation of this idea is the decision-estimation coefficient (DEC), which was shown to provide nearly tight lower and upper bounds on the worst-case expected regret in structured bandits and reinforcement learning. By re-parametrizing the offset DEC with the confidence radius and solving the corresponding min-max program, we derive an anytime variant of the Estimation-To-Decisions algorithm (Anytime-E2D). Importantly, the algorithm optimizes the exploration-exploitation trade-off online instead of via the analysis. Our formulation leads to a practical algorithm for finite model classes and linear feedback models. We further point out connections to the information ratio, decoupling coefficient and PAC-DEC, and numerically evaluate the performance of E2D on simple examples.

Contextual optimization, also known as predict-then-optimize or prescriptive analytics, considers an optimization problem with the presence of covariates (context or side information). The goal is to learn a prediction model (from the training data) that predicts the objective function from the covariates, and then in the test phase, solve the optimization problem with the covariates but without the observation of the objective function. In this paper, we consider a risk-sensitive version of the problem and propose a generic algorithm design paradigm called predict-then-calibrate. The idea is to first develop a prediction model without concern for the downstream risk profile or robustness guarantee, and then utilize calibration (or recalibration) methods to quantify the uncertainty of the prediction. While the existing methods suffer from either a restricted choice of the prediction model or strong assumptions on the underlying data, we show the disentangling of the prediction model and the calibration/uncertainty quantification has several advantages. First, it imposes no restriction on the prediction model and thus fully unleashes the potential of off-the-shelf machine learning methods. Second, the derivation of the risk and robustness guarantee can be made independent of the choice of the prediction model through a data-splitting idea. Third, our paradigm of predict-then-calibrate applies to both (risk-sensitive) robust and (risk-neutral) distributionally robust optimization (DRO) formulations. Theoretically, it gives new generalization bounds for the contextual LP problem and sheds light on the existing results of DRO for contextual LP. Numerical experiments further reinforce the advantage of the predict-then-calibrate paradigm in that an improvement on either the prediction model or the calibration model will lead to a better final performance.

We present improved algorithms with worst-case regret guarantees for the stochastic linear bandit problem. The widely used "optimism in the face of uncertainty" principle reduces a stochastic bandit problem to the construction of a confidence sequence for the unknown reward function. The performance of the resulting bandit algorithm depends on the size of the confidence sequence, with smaller confidence sets yielding better empirical performance and stronger regret guarantees. In this work, we use a novel tail bound for adaptive martingale mixtures to construct confidence sequences which are suitable for stochastic bandits. These confidence sequences allow for efficient action selection via convex programming. We prove that a linear bandit algorithm based on our confidence sequences is guaranteed to achieve competitive worst-case regret. We show that our confidence sequences are tighter than competitors, both empirically and theoretically. Finally, we demonstrate that our tighter confidence sequences give improved performance in several hyperparameter tuning tasks.

The minimax problems arise throughout machine learning applications, ranging from adversarial training and policy evaluation in reinforcement learning to AUROC maximization. To address the large-scale distributed data challenges across multiple clients with communication-efficient distributed training, federated learning (FL) is gaining popularity. Many optimization algorithms for minimax problems have been developed in the centralized setting (\emph{i.e.}, single-machine). Nonetheless, the algorithm for minimax problems under FL is still underexplored. In this paper, we study a class of federated nonconvex minimax optimization problems. We propose FL algorithms (FedSGDA+ and FedSGDA-M) and reduce existing complexity results for the most common minimax problems. For nonconvex-concave problems, we propose FedSGDA+ and reduce the communication complexity to $O(\varepsilon^{-6})$. Under nonconvex-strongly-concave and nonconvex-PL minimax settings, we prove that FedSGDA-M has the best-known sample complexity of $O(\kappa^{3} N^{-1}\varepsilon^{-3})$ and the best-known communication complexity of $O(\kappa^{2}\varepsilon^{-2})$. FedSGDA-M is the first algorithm to match the best sample complexity $O(\varepsilon^{-3})$ achieved by the single-machine method under the nonconvex-strongly-concave setting. Extensive experimental results on fair classification and AUROC maximization show the efficiency of our algorithms.

Finite-difference methods are a class of algorithms designed to solve black-box optimization problems by approximating a gradient of the target function on a set of directions. In black-box optimization, the non-smooth setting is particularly relevant since, in practice, differentiability and smoothness assumptions cannot be verified. To cope with nonsmoothness, several authors use a smooth approximation of the target function and show that finite difference methods approximate its gradient. Recently, it has been proved that imposing a structure in the directions allows improving performance. However, only the smooth setting was considered. To close this gap, we introduce and analyze O-ZD, the first structured finite-difference algorithm for non-smooth black-box optimization. Our method exploits a smooth approximation of the target function and we prove that it approximates its gradient on a subset of random {\em orthogonal} directions. We analyze the convergence of O-ZD under different assumptions. For non-smooth convex functions, we obtain the optimal complexity. In the non-smooth non-convex setting, we characterize the number of iterations needed to bound the expected norm of the smoothed gradient. For smooth functions, our analysis recovers existing results for structured zeroth-order methods for the convex case and extends them to the non-convex setting. We conclude with numerical simulations where assumptions are satisfied, observing that our algorithm has very good practical performances.

Sharpness-aware minimization (SAM) has well documented merits in enhancing generalization of deep neural networks, even without sizable data augmentation. Embracing the geometry of the loss function, where neighborhoods of 'flat minima' heighten generalization ability, SAM seeks 'flat valleys' by minimizing the maximum loss caused by an *adversary* perturbing parameters within the neighborhood. Although critical to account for sharpness of the loss function, such an '*over-friendly* adversary' can curtail the outmost level of generalization. The novel approach of this contribution fosters stabilization of adversaries through *variance suppression* (VaSSO) to avoid such friendliness. VaSSO's *provable* stability safeguards its numerical improvement over SAM in model-agnostic tasks, including image classification and machine translation. In addition, experiments confirm that VaSSO endows SAM with robustness against high levels of label noise. Code is available at https://github.com/BingcongLi/VaSSO.

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This framework extends classical stochastic bilevel optimization when the lower-level decision maker responds optimally not only to the decision of the upper-level decision maker but also to some side information and when there are multiple or even infinite many followers. It captures important applications such as meta-learning, personalized federated learning, end-to-end learning, and Wasserstein distributionally robust optimization with side information (WDRO-SI). Due to the presence of contextual information, existing single-loop methods for classical stochastic bilevel optimization are unable to converge. To overcome this challenge, we introduce an efficient double-loop gradient method based on the Multilevel Monte-Carlo (MLMC) technique and establish its sample and computational complexities. When specialized to stochastic nonconvex optimization, our method matches existing lower bounds. For meta-learning, the complexity of our method does not depend on the number of tasks. Numerical experiments further validate our theoretical results.

Policy gradient lies at the core of deep reinforcement learning (RL) in continuous domains. Despite much success, it is often observed in practice that RL training with policy gradient can fail for many reasons, even on standard control problems with known solutions. We propose a framework for understanding one inherent limitation of the policy gradient approach: the optimization landscape in the policy space can be extremely non-smooth or fractal for certain classes of MDPs, such that there does not exist gradient to be estimated in the first place. We draw on techniques from chaos theory and non-smooth analysis, and analyze the maximal Lyapunov exponents and H\"older exponents of the policy optimization objectives. Moreover, we develop a practical method that can estimate the local smoothness of objective function from samples to identify when the training process has encountered fractal landscapes. We show experiments to illustrate how some failure cases of policy optimization can be explained by such fractal landscapes.

Designing reward functions for efficiently guiding reinforcement learning (RL) agents toward specific behaviors is a complex task. This is challenging since it requires the identification of reward structures that are not sparse and that avoid inadvertently inducing undesirable behaviors. Naively modifying the reward structure to offer denser and more frequent feedback can lead to unintended outcomes and promote behaviors that are not aligned with the designer's intended goal. Although potential-based reward shaping is often suggested as a remedy, we systematically investigate settings where deploying it often significantly impairs performance. To address these issues, we introduce a new framework that uses a bi-level objective to learn \emph{behavior alignment reward functions}. These functions integrate auxiliary rewards reflecting a designer's heuristics and domain knowledge with the environment's primary rewards. Our approach automatically determines the most effective way to blend these types of feedback, thereby enhancing robustness against heuristic reward misspecification. Remarkably, it can also adapt an agent's policy optimization process to mitigate suboptimalities resulting from limitations and biases inherent in the underlying RL algorithms. We evaluate our method's efficacy on a diverse set of tasks, from small-scale experiments to high-dimensional control challenges. We investigate heuristic auxiliary rewards of varying quality---some of which are beneficial and others detrimental to the learning process. Our results show that our framework offers a robust and principled way to integrate designer-specified heuristics. It not only addresses key shortcomings of existing approaches but also consistently leads to high-performing solutions, even when given misaligned or poorly-specified auxiliary reward functions.

In this paper, we hypothesize that gradient-based meta-learning (GBML) implicitly suppresses the Hessian along the optimization trajectory in the inner loop. Based on this hypothesis, we introduce an algorithm called SHOT (Suppressing the Hessian along the Optimization Trajectory) that minimizes the distance between the parameters of the target and reference models to suppress the Hessian in the inner loop. Despite dealing with high-order terms, SHOT does not increase the computational complexity of the baseline model much. It is agnostic to both the algorithm and architecture used in GBML, making it highly versatile and applicable to any GBML baseline. To validate the effectiveness of SHOT, we conduct empirical tests on standard few-shot learning tasks and qualitatively analyze its dynamics. We confirm our hypothesis empirically and demonstrate that SHOT outperforms the corresponding baseline.