arXiv subjects

Kaiqing Zhang

Publications and source records attributed to Kaiqing Zhang.

At least 55 records · Page 3Linked to original sources

arXiv2023

Learning to Extrapolate: A Transductive Approach

Machine learning systems, especially with overparameterized deep neural networks, can generalize to novel test instances drawn from the same distribution as the training data. However, they fare poorly when evaluated on out-of-support test points. In this work, we tackle the problem of developing machine learning systems that retain the power of overparameterized function approximators while enabling extrapolation to out-of-support test points when possible. This is accomplished by noting that under certain conditions, a "transductive" reparameterization can convert an out-of-support extrapolation problem into a problem of within-support combinatorial generalization. We propose a simple strategy based on bilinear embeddings to enable this type of combinatorial generalization, thereby addressing the out-of-support extrapolation problem under certain conditions. We instantiate a simple, practical algorithm applicable to various supervised learning and imitation learning tasks.

cs.LG↗

arXiv2023

Symmetric (Optimistic) Natural Policy Gradient for Multi-agent Learning with Parameter Convergence

Multi-agent interactions are increasingly important in the context of reinforcement learning, and the theoretical foundations of policy gradient methods have attracted surging research interest. We investigate the global convergence of natural policy gradient (NPG) algorithms in multi-agent learning. We first show that vanilla NPG may not have parameter convergence, i.e., the convergence of the vector that parameterizes the policy, even when the costs are regularized (which enabled strong convergence guarantees in the policy space in the literature). This non-convergence of parameters leads to stability issues in learning, which becomes especially relevant in the function approximation setting, where we can only operate on low-dimensional parameters, instead of the high-dimensional policy. We then propose variants of the NPG algorithm, for several standard multi-agent learning scenarios: two-player zero-sum matrix and Markov games, and multi-player monotone games, with global last-iterate parameter convergence guarantees. We also generalize the results to certain function approximation settings. Note that in our algorithms, the agents take symmetric roles. Our results might also be of independent interest for solving nonconvex-nonconcave minimax optimization problems with certain structures. Simulations are also provided to corroborate our theoretical findings.

math.OC↗

arXiv2023

A Finite-Sample Analysis of Payoff-Based Independent Learning in Zero-Sum Stochastic Games

We study two-player zero-sum stochastic games, and propose a form of independent learning dynamics called Doubly Smoothed Best-Response dynamics, which integrates a discrete and doubly smoothed variant of the best-response dynamics into temporal-difference (TD)-learning and minimax value iteration. The resulting dynamics are payoff-based, convergent, rational, and symmetric among players. Our main results provide finite-sample guarantees. In particular, we prove the first-known $\tilde{\mathcal{O}}(1/ε^2)$ sample complexity bound for payoff-based independent learning dynamics, up to a smoothing bias. In the special case where the stochastic game has only one state (i.e., matrix games), we provide a sharper $\tilde{\mathcal{O}}(1/ε)$ sample complexity. Our analysis uses a novel coupled Lyapunov drift approach to capture the evolution of multiple sets of coupled and stochastic iterates, which might be of independent interest.

cs.GT↗

arXiv2023

Does Learning from Decentralized Non-IID Unlabeled Data Benefit from Self Supervision?

Decentralized learning has been advocated and widely deployed to make efficient use of distributed datasets, with an extensive focus on supervised learning (SL) problems. Unfortunately, the majority of real-world data are unlabeled and can be highly heterogeneous across sources. In this work, we carefully study decentralized learning with unlabeled data through the lens of self-supervised learning (SSL), specifically contrastive visual representation learning. We study the effectiveness of a range of contrastive learning algorithms under decentralized learning settings, on relatively large-scale datasets including ImageNet-100, MS-COCO, and a new real-world robotic warehouse dataset. Our experiments show that the decentralized SSL (Dec-SSL) approach is robust to the heterogeneity of decentralized datasets, and learns useful representation for object classification, detection, and segmentation tasks. This robustness makes it possible to significantly reduce communication and reduce the participation ratio of data sources with only minimal drops in performance. Interestingly, using the same amount of data, the representation learned by Dec-SSL can not only perform on par with that learned by centralized SSL which requires communication and excessive data storage costs, but also sometimes outperform representations extracted from decentralized SL which requires extra knowledge about the data labels. Finally, we provide theoretical insights into understanding why data heterogeneity is less of a concern for Dec-SSL objectives, and introduce feature alignment and clustering techniques to develop a new Dec-SSL algorithm that further improves the performance, in the face of highly non-IID data. Our study presents positive evidence to embrace unlabeled data in decentralized learning, and we hope to provide new insights into whether and why decentralized SSL is effective.

cs.LG↗

arXiv2022

An Improved Analysis of (Variance-Reduced) Policy Gradient and Natural Policy Gradient Methods

In this paper, we revisit and improve the convergence of policy gradient (PG), natural PG (NPG) methods, and their variance-reduced variants, under general smooth policy parametrizations. More specifically, with the Fisher information matrix of the policy being positive definite: i) we show that a state-of-the-art variance-reduced PG method, which has only been shown to converge to stationary points, converges to the globally optimal value up to some inherent function approximation error due to policy parametrization; ii) we show that NPG enjoys a lower sample complexity; iii) we propose SRVR-NPG, which incorporates variance-reduction into the NPG update. Our improvements follow from an observation that the convergence of (variance-reduced) PG and NPG methods can improve each other: the stationary convergence analysis of PG can be applied to NPG as well, and the global convergence analysis of NPG can help to establish the global convergence of (variance-reduced) PG methods. Our analysis carefully integrates the advantages of these two lines of works. Thanks to this improvement, we have also made variance-reduction for NPG possible, with both global convergence and an efficient finite-sample complexity.

cs.LG↗

arXiv2022

Mechanical properties of AlMgB14-related boron carbide structures. A first principle study

We examine the effects produced by replacing B-B interlayer bonds by C-C bonds in AlMgB14-related boron network on its mechanical properties. The elastic constants, Vickers hardness and shear strength are evaluated by means of first principle computer simulations on the basis of density functional theory. The results of simulations suggest a possibility of existence of several orthorhombic boron carbide phases with strongly enhanced mechanical properties with the Young modulus and Vickers hardness being within the range of 550-600 GPa and 43-50 GPa, respectively

cond-mat.mtrl-sci↗

arXiv2022

Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies

Gradient-based methods have been widely used for system design and optimization in diverse application domains. Recently, there has been a renewed interest in studying theoretical properties of these methods in the context of control and reinforcement learning. This article surveys some of the recent developments on policy optimization, a gradient-based iterative approach for feedback control synthesis, popularized by successes of reinforcement learning. We take an interdisciplinary perspective in our exposition that connects control theory, reinforcement learning, and large-scale optimization. We review a number of recently-developed theoretical results on the optimization landscape, global convergence, and sample complexity of gradient-based methods for various continuous control problems such as the linear quadratic regulator (LQR), $\mathcal{H}_\infty$ control, risk-sensitive control, linear quadratic Gaussian (LQG) control, and output feedback synthesis. In conjunction with these optimization results, we also discuss how direct policy optimization handles stability and robustness concerns in learning-based control, two main desiderata in control engineering. We conclude the survey by pointing out several challenges and opportunities at the intersection of learning and control.

math.OC↗

arXiv2022

Do Differentiable Simulators Give Better Policy Gradients?

Differentiable simulators promise faster computation time for reinforcement learning by replacing zeroth-order gradient estimates of a stochastic objective with an estimate based on first-order gradients. However, it is yet unclear what factors decide the performance of the two estimators on complex landscapes that involve long-horizon planning and control on physical systems, despite the crucial relevance of this question for the utility of differentiable simulators. We show that characteristics of certain physical systems, such as stiffness or discontinuities, may compromise the efficacy of the first-order estimator, and analyze this phenomenon through the lens of bias and variance. We additionally propose an $α$-order gradient estimator, with $α\in [0,1]$, which correctly utilizes exact gradients to combine the efficiency of first-order estimates with the robustness of zero-order methods. We demonstrate the pitfalls of traditional estimators and the advantages of the $α$-order estimator on some numerical examples.

cs.LG↗

arXiv2022

Model-Free Non-Stationary RL: Near-Optimal Regret and Applications in Multi-Agent RL and Inventory Control

We consider model-free reinforcement learning (RL) in non-stationary Markov decision processes. Both the reward functions and the state transition functions are allowed to vary arbitrarily over time as long as their cumulative variations do not exceed certain variation budgets. We propose Restarted Q-Learning with Upper Confidence Bounds (RestartQ-UCB), the first model-free algorithm for non-stationary RL, and show that it outperforms existing solutions in terms of dynamic regret. Specifically, RestartQ-UCB with Freedman-type bonus terms achieves a dynamic regret bound of $\widetilde{O}(S^{\frac{1}{3}} A^{\frac{1}{3}} Δ^{\frac{1}{3}} H T^{\frac{2}{3}})$, where $S$ and $A$ are the numbers of states and actions, respectively, $Δ>0$ is the variation budget, $H$ is the number of time steps per episode, and $T$ is the total number of time steps. We further present a parameter-free algorithm named Double-Restart Q-UCB that does not require prior knowledge of the variation budget. We show that our algorithms are \emph{nearly optimal} by establishing an information-theoretical lower bound of $Ω(S^{\frac{1}{3}} A^{\frac{1}{3}} Δ^{\frac{1}{3}} H^{\frac{2}{3}} T^{\frac{2}{3}})$, the first lower bound in non-stationary RL. Numerical experiments validate the advantages of RestartQ-UCB in terms of both cumulative rewards and computational efficiency. We demonstrate the power of our results in examples of multi-agent RL and inventory control across related products.

cs.LG↗

arXiv2022

Independent Policy Gradient for Large-Scale Markov Potential Games: Sharper Rates, Function Approximation, and Game-Agnostic Convergence

We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space and/or the number of players can be very large, we propose new independent policy gradient algorithms that are run by all players in tandem. When there is no uncertainty in the gradient evaluation, we show that our algorithm finds an $ε$-Nash equilibrium with $O(1/ε^2)$ iteration complexity which does not explicitly depend on the state space size. When the exact gradient is not available, we establish $O(1/ε^5)$ sample complexity bound in a potentially infinitely large state space for a sample-based algorithm that utilizes function approximation. Moreover, we identify a class of independent policy gradient algorithms that enjoys convergence for both zero-sum Markov games and Markov cooperative games with the players that are oblivious to the types of games being played. Finally, we provide computational experiments to corroborate the merits and the effectiveness of our theoretical developments.

cs.LG↗

arXiv2022

What is a Good Metric to Study Generalization of Minimax Learners?

Minimax optimization has served as the backbone of many machine learning (ML) problems. Although the convergence behavior of optimization algorithms has been extensively studied in the minimax settings, their generalization guarantees in stochastic minimax optimization problems, i.e., how the solution trained on empirical data performs on unseen testing data, have been relatively underexplored. A fundamental question remains elusive: What is a good metric to study generalization of minimax learners? In this paper, we aim to answer this question by first showing that primal risk, a universal metric to study generalization in minimization problems, which has also been adopted recently to study generalization in minimax ones, fails in simple examples. We thus propose a new metric to study generalization of minimax learners: the primal gap, defined as the difference between the primal risk and its minimum over all models, to circumvent the issues. Next, we derive generalization error bounds for the primal gap in nonconvex-concave settings. As byproducts of our analysis, we also solve two open questions: establishing generalization error bounds for primal risk and primal-dual risk, another existing metric that is only well-defined when the global saddle-point exists, in the strong sense, i.e., without strong concavity or assuming that the maximization and expectation can be interchanged, while either of these assumptions was needed in the literature. Finally, we leverage this new metric to compare the generalization behavior of two popular algorithms -- gradient descent-ascent (GDA) and gradient descent-max (GDMax) in stochastic minimax optimization.

stat.ML↗

arXiv2022

Byzantine-Robust Online and Offline Distributed Reinforcement Learning

We consider a distributed reinforcement learning setting where multiple agents separately explore the environment and communicate their experiences through a central server. However, $α$-fraction of agents are adversarial and can report arbitrary fake information. Critically, these adversarial agents can collude and their fake data can be of any sizes. We desire to robustly identify a near-optimal policy for the underlying Markov decision process in the presence of these adversarial agents. Our main technical contribution is Weighted-Clique, a novel algorithm for the robust mean estimation from batches problem, that can handle arbitrary batch sizes. Building upon this new estimator, in the offline setting, we design a Byzantine-robust distributed pessimistic value iteration algorithm; in the online setting, we design a Byzantine-robust distributed optimistic value iteration algorithm. Both algorithms obtain near-optimal sample complexities and achieve superior robustness guarantee than prior works.

cs.LG↗

arXiv2022

Fictitious Play in Markov Games with Single Controller

Certain but important classes of strategic-form games, including zero-sum and identical-interest games, have the fictitious-play-property (FPP), i.e., beliefs formed in fictitious play dynamics always converge to a Nash equilibrium (NE) in the repeated play of these games. Such convergence results are seen as a (behavioral) justification for the game-theoretical equilibrium analysis. Markov games (MGs), also known as stochastic games, generalize the repeated play of strategic-form games to dynamic multi-state settings with Markovian state transitions. In particular, MGs are standard models for multi-agent reinforcement learning -- a reviving research area in learning and games, and their game-theoretical equilibrium analyses have also been conducted extensively. However, whether certain classes of MGs have the FPP or not (i.e., whether there is a behavioral justification for equilibrium analysis or not) remains largely elusive. In this paper, we study a new variant of fictitious play dynamics for MGs and show its convergence to an NE in n-player identical-interest MGs in which a single player controls the state transitions. Such games are of interest in communications, control, and economics applications. Our result together with the recent results in [Sayin et al. 2020] establishes the FPP of two-player zero-sum MGs and n-player identical-interest MGs with a single controller (standing at two different ends of the MG spectrum from fully competitive to fully cooperative).

cs.GT↗

arXiv2022

Design and Commissioning of A Beam Distribution System for Multiple Undulator Line Operation of the SXFEL-UF

As an important measure of improving the efficiency and usability of X-ray free electron laser facilities, simultaneous operation of multiple undulator lines realized by a beam distribution system has become a standard configuration in the recent built XFEL facilities. In Shanghai, SXFEL-UF, the first soft X-ray free electron laser user facility in China, has finished construction and started commissioning recently. Electron beam from linac is alternately distributed between the two parallel undulator beam lines by a beam distribution system with a 6° deflection line. The beam distribution system is designed to keep the beam properties like low emittance, high peak charge and small bunch length from being spoiled. Beam collective effects such as the dispersion, coherent synchrotron radiation and micro-bunching instability should be well suppressed to guarantee the beam quality. In this work, the detailed physics design of the beam distribution system is described and the recent commissioning result is reported.

physics.acc-ph↗

arXiv2022

The Complexity of Markov Equilibrium in Stochastic Games

We show that computing approximate stationary Markov coarse correlated equilibria (CCE) in general-sum stochastic games is computationally intractable, even when there are two players, the game is turn-based, the discount factor is an absolute constant, and the approximation is an absolute constant. Our intractability results stand in sharp contrast to normal-form games where exact CCEs are efficiently computable. A fortiori, our results imply that there are no efficient algorithms for learning stationary Markov CCE policies in multi-agent reinforcement learning (MARL), even when the interaction is two-player and turn-based, and both the discount factor and the desired approximation of the learned policies is an absolute constant. In turn, these results stand in sharp contrast to single-agent reinforcement learning (RL) where near-optimal stationary Markov policies can be efficiently learned. Complementing our intractability results for stationary Markov CCEs, we provide a decentralized algorithm (assuming shared randomness among players) for learning a nonstationary Markov CCE policy with polynomial time and sample complexity in all problem parameters. Previous work for learning Markov CCE policies all required exponential time and sample complexity in the number of players.

cs.LG↗

arXiv2022

Towards Understanding Asynchronous Advantage Actor-critic: Convergence and Linear Speedup

Asynchronous and parallel implementation of standard reinforcement learning (RL) algorithms is a key enabler of the tremendous success of modern RL. Among many asynchronous RL algorithms, arguably the most popular and effective one is the asynchronous advantage actor-critic (A3C) algorithm. Although A3C is becoming the workhorse of RL, its theoretical properties are still not well-understood, including its non-asymptotic analysis and the performance gain of parallelism (a.k.a. linear speedup). This paper revisits the A3C algorithm and establishes its non-asymptotic convergence guarantees. Under both i.i.d. and Markovian sampling, we establish the local convergence guarantee for A3C in the general policy approximation case and the global convergence guarantee in softmax policy parameterization. Under i.i.d. sampling, A3C obtains sample complexity of $\mathcal{O}(ε^{-2.5}/N)$ per worker to achieve $ε$ accuracy, where $N$ is the number of workers. Compared to the best-known sample complexity of $\mathcal{O}(ε^{-2.5})$ for two-timescale AC, A3C achieves \emph{linear speedup}, which justifies the advantage of parallelism and asynchrony in AC algorithms theoretically for the first time. Numerical tests on synthetic environment, OpenAI Gym environments and Atari games have been provided to verify our theoretical analysis.

cs.LG↗

arXiv2022

Globally Convergent Policy Search over Dynamic Filters for Output Estimation

We introduce the first direct policy search algorithm which provably converges to the globally optimal $\textit{dynamic}$ filter for the classical problem of predicting the outputs of a linear dynamical system, given noisy, partial observations. Despite the ubiquity of partial observability in practice, theoretical guarantees for direct policy search algorithms, one of the backbones of modern reinforcement learning, have proven difficult to achieve. This is primarily due to the degeneracies which arise when optimizing over filters that maintain internal state. In this paper, we provide a new perspective on this challenging problem based on the notion of $\textit{informativity}$, which intuitively requires that all components of a filter's internal state are representative of the true state of the underlying dynamical system. We show that informativity overcomes the aforementioned degeneracy. Specifically, we propose a $\textit{regularizer}$ which explicitly enforces informativity, and establish that gradient descent on this regularized objective - combined with a ``reconditioning step'' - converges to the globally optimal cost a $\mathcal{O}(1/T)$ rate. Our analysis relies on several new results which may be of independent interest, including a new framework for analyzing non-convex gradient descent via convex reformulation, and novel bounds on the solution to linear Lyapunov equations in terms of (our quantitative measure of) informativity.

math.OC↗

arXiv2022

On Improving Model-Free Algorithms for Decentralized Multi-Agent Reinforcement Learning

Multi-agent reinforcement learning (MARL) algorithms often suffer from an exponential sample complexity dependence on the number of agents, a phenomenon known as \emph{the curse of multiagents}. In this paper, we address this challenge by investigating sample-efficient model-free algorithms in \emph{decentralized} MARL, and aim to improve existing algorithms along this line. For learning (coarse) correlated equilibria in general-sum Markov games, we propose \emph{stage-based} V-learning algorithms that significantly simplify the algorithmic design and analysis of recent works, and circumvent a rather complicated no-\emph{weighted}-regret bandit subroutine. For learning Nash equilibria in Markov potential games, we propose an independent policy gradient algorithm with a decentralized momentum-based variance reduction technique. All our algorithms are decentralized in that each agent can make decisions based on only its local information. Neither communication nor centralized coordination is required during learning, leading to a natural generalization to a large number of agents. We also provide numerical simulations to corroborate our theoretical findings.

cs.LG↗