arXiv subjects

Kaiqing Zhang

Publications and source records attributed to Kaiqing Zhang.

At least 73 records · Page 4Linked to original sources

arXiv2021

Derivative-Free Policy Optimization for Linear Risk-Sensitive and Robust Control Design: Implicit Regularization and Sample Complexity

Direct policy search serves as one of the workhorses in modern reinforcement learning (RL), and its applications in continuous control tasks have recently attracted increasing attention. In this work, we investigate the convergence theory of policy gradient (PG) methods for learning the linear risk-sensitive and robust controller. In particular, we develop PG methods that can be implemented in a derivative-free fashion by sampling system trajectories, and establish both global convergence and sample complexity results in the solutions of two fundamental settings in risk-sensitive and robust control: the finite-horizon linear exponential quadratic Gaussian, and the finite-horizon linear-quadratic disturbance attenuation problems. As a by-product, our results also provide the first sample complexity for the global convergence of PG methods on solving zero-sum linear-quadratic dynamic games, a nonconvex-nonconcave minimax optimization problem that serves as a baseline setting in multi-agent reinforcement learning (MARL) with continuous spaces. One feature of our algorithms is that during the learning phase, a certain level of robustness/risk-sensitivity of the controller is preserved, which we termed as the implicit regularization property, and is an essential requirement in safety-critical control systems.

math.OC↗

arXiv2021

Decentralized Q-Learning in Zero-sum Markov Games

We study multi-agent reinforcement learning (MARL) in infinite-horizon discounted zero-sum Markov games. We focus on the practical but challenging setting of decentralized MARL, where agents make decisions without coordination by a centralized controller, but only based on their own payoffs and local actions executed. The agents need not observe the opponent's actions or payoffs, possibly being even oblivious to the presence of the opponent, nor be aware of the zero-sum structure of the underlying game, a setting also referred to as radically uncoupled in the literature of learning in games. In this paper, we develop a radically uncoupled Q-learning dynamics that is both rational and convergent: the learning dynamics converges to the best response to the opponent's strategy when the opponent follows an asymptotically stationary strategy; when both agents adopt the learning dynamics, they converge to the Nash equilibrium of the game. The key challenge in this decentralized setting is the non-stationarity of the environment from an agent's perspective, since both her own payoffs and the system evolution depend on the actions of other agents, and each agent adapts her policies simultaneously and independently. To address this issue, we develop a two-timescale learning dynamics where each agent updates her local Q-function and value function estimates concurrently, with the latter happening at a slower timescale.

cs.GT↗

arXiv2021

Independent Learning in Stochastic Games

Reinforcement learning (RL) has recently achieved tremendous successes in many artificial intelligence applications. Many of the forefront applications of RL involve multiple agents, e.g., playing chess and Go games, autonomous driving, and robotics. Unfortunately, the framework upon which classical RL builds is inappropriate for multi-agent learning, as it assumes an agent's environment is stationary and does not take into account the adaptivity of other agents. In this review paper, we present the model of stochastic games for multi-agent learning in dynamic environments. We focus on the development of simple and independent learning dynamics for stochastic games: each agent is myopic and chooses best-response type actions to other agents' strategy without any coordination with her opponent. There has been limited progress on developing convergent best-response type independent learning dynamics for stochastic games. We present our recently proposed simple and independent learning dynamics that guarantee convergence in zero-sum stochastic games, together with a review of other contemporaneous algorithms for dynamic multi-agent learning in this setting. Along the way, we also reexamine some classical results from both the game theory and RL literature, to situate both the conceptual contributions of our independent learning dynamics, and the mathematical novelties of our analysis. We hope this review paper serves as an impetus for the resurgence of studying independent and natural learning dynamics in game theory, for the more challenging settings with a dynamic environment.

cs.GT↗

arXiv2021

Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms

Recent years have witnessed significant advances in reinforcement learning (RL), which has registered great success in solving various sequential decision-making problems in machine learning. Most of the successful RL applications, e.g., the games of Go and Poker, robotics, and autonomous driving, involve the participation of more than one single agent, which naturally fall into the realm of multi-agent RL (MARL), a domain with a relatively long history, and has recently re-emerged due to advances in single-agent RL techniques. Though empirically successful, theoretical foundations for MARL are relatively lacking in the literature. In this chapter, we provide a selective overview of MARL, with focus on algorithms backed by theoretical analysis. More specifically, we review the theoretical results of MARL algorithms mainly within two representative frameworks, Markov/stochastic games and extensive-form games, in accordance with the types of tasks they address, i.e., fully cooperative, fully competitive, and a mix of the two. We also introduce several significant but challenging applications of these algorithms. Orthogonal to the existing reviews on MARL, we highlight several new angles and taxonomies of MARL theory, including learning in extensive-form games, decentralized MARL with networked agents, MARL in the mean-field regime, (non-)convergence of policy-based methods for learning in games, etc. Some of the new angles extrapolate from our own research endeavors and interests. Our overall goal with this chapter is, beyond providing an assessment of the current state of the field on the mark, to identify fruitful future research directions on theoretical studies of MARL. We expect this chapter to serve as continuing stimulus for researchers interested in working on this exciting while challenging topic.

cs.LG↗

arXiv2021

Communication-Efficient Policy Gradient Methods for Distributed Reinforcement Learning

This paper deals with distributed policy optimization in reinforcement learning, which involves a central controller and a group of learners. In particular, two typical settings encountered in several applications are considered: multi-agent reinforcement learning (RL) and parallel RL, where frequent information exchanges between the learners and the controller are required. For many practical distributed systems, however, the overhead caused by these frequent communication exchanges is considerable, and becomes the bottleneck of the overall performance. To address this challenge, a novel policy gradient approach is developed for solving distributed RL. The novel approach adaptively skips the policy gradient communication during iterations, and can reduce the communication overhead without degrading learning performance. It is established analytically that: i) the novel algorithm has convergence rate identical to that of the plain-vanilla policy gradient; while ii) if the distributed learners are heterogeneous in terms of their reward functions, the number of communication rounds needed to achieve a desirable learning accuracy is markedly reduced. Numerical experiments corroborate the communication reduction attained by the novel algorithm compared to alternatives.

cs.LG↗

arXiv2021

Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates

We study the multi-agent safe control problem where agents should avoid collisions to static obstacles and collisions with each other while reaching their goals. Our core idea is to learn the multi-agent control policy jointly with learning the control barrier functions as safety certificates. We propose a novel joint-learning framework that can be implemented in a decentralized fashion, with generalization guarantees for certain function classes. Such a decentralized framework can adapt to an arbitrarily large number of agents. Building upon this framework, we further improve the scalability by incorporating neural network architectures that are invariant to the quantity and permutation of neighboring agents. In addition, we propose a new spontaneous policy refinement method to further enforce the certificate condition during testing. We provide extensive experiments to demonstrate that our method significantly outperforms other leading multi-agent control approaches in terms of maintaining safety and completing original tasks. Our approach also shows exceptional generalization capability in that the control policy can be trained with 8 agents in one scenario, while being used on other scenarios with up to 1024 agents in complex multi-agent environments and dynamics.

cs.MA↗

arXiv2021

Policy Optimization for $\mathcal{H}_2$ Linear Control with $\mathcal{H}_\infty$ Robustness Guarantee: Implicit Regularization and Global Convergence

Policy optimization (PO) is a key ingredient for reinforcement learning (RL). For control design, certain constraints are usually enforced on the policies to optimize, accounting for either the stability, robustness, or safety concerns on the system. Hence, PO is by nature a constrained (nonconvex) optimization in most cases, whose global convergence is challenging to analyze in general. More importantly, some constraints that are safety-critical, e.g., the $\mathcal{H}_\infty$-norm constraint that guarantees the system robustness, are difficult to enforce as the PO methods proceed. Recently, policy gradient methods have been shown to converge to the global optimum of linear quadratic regulator (LQR), a classical optimal control problem, without regularizing/projecting the control iterates onto the stabilizing set, its (implicit) feasible set. This striking result is built upon the coercive property of the cost, ensuring that the iterates remain feasible as the cost decreases. In this paper, we study the convergence theory of PO for $\mathcal{H}_2$ linear control with $\mathcal{H}_\infty$-norm robustness guarantee. One significant new feature of this problem is the lack of coercivity, i.e., the cost may have finite value around the feasible set boundary, breaking the existing analysis for LQR. Interestingly, we show that two PO methods enjoy the implicit regularization property, i.e., the iterates preserve the $\mathcal{H}_\infty$ robustness constraint as if they are regularized by the algorithms. Furthermore, despite the nonconvexity of the problem, we show that these algorithms converge to the globally optimal policies with globally sublinear rates, avoiding all suboptimal stationary points/local minima, and with locally (super-)linear rates under certain conditions.

math.OC↗

arXiv2021

Self-Amplification of Coherent Energy Modulation in Seeded Free-Electron Lasers

The spectroscopic techniques for time-resolved fine analysis of matter require coherent X-ray radiation with femtosecond duration and high average brightness. Seeded free-electron lasers (FELs), which use the frequency up-conversion of an external seed laser to improve temporal coherence, are ideal for providing fully coherent soft X-ray pulses. However, it is difficult to operate seeded FELs at a high repetition rate due to the limitations of present state-of-the-art laser systems. Here, we report the novel self-modulation method for enhancing laser-induced energy modulation, thereby significantly reducing the requirement of an external laser system. Driven by this scheme, we experimentally realize high harmonic generation in a seeded FEL using an unprecedentedly small energy modulation. An electron beam with a laser-induced energy modulation as small as 1.8 times the slice energy spread is used for lasing at the 7th harmonic of a 266-nm seed laser in a single-stage high-gain harmonic generation (HGHG) setup and the 30th harmonic of the seed laser in a two-stage HGHG setup. The results mark a major step towards a high-repetition-rate, fully coherent X-ray FEL.

physics.acc-ph↗

arXiv2021

Policy Optimization Provably Converges to Nash Equilibria in Zero-Sum Linear Quadratic Games

We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave saddle-point problem in the policy space. Specifically, we show that despite its nonconvexity and nonconcavity, zero-sum LQ games have the property that the stationary point of the objective function with respect to the linear feedback control policies constitutes the NE of the game. Building upon this, we develop three projected nested-gradient methods that are guaranteed to converge to the NE of the game. Moreover, we show that all of these algorithms enjoy both globally sublinear and locally linear convergence rates. Simulation results are also provided to illustrate the satisfactory convergence properties of the algorithms. To the best of our knowledge, this work appears to be the first one to investigate the optimization landscape of LQ games, and provably show the convergence of policy optimization methods to the Nash equilibria. Our work serves as an initial step toward understanding the theoretical aspects of policy-based reinforcement learning algorithms for zero-sum Markov games in general.

cs.LG↗

arXiv2021

Fully Asynchronous Policy Evaluation in Distributed Reinforcement Learning over Networks

This paper proposes a \emph{fully asynchronous} scheme for the policy evaluation problem of distributed reinforcement learning (DisRL) over directed peer-to-peer networks. Without waiting for any other node of the network, each node can locally update its value function at any time by using (possibly delayed) information from its neighbors. This is in sharp contrast to the gossip-based scheme where a pair of nodes concurrently update. Though the fully asynchronous setting involves a difficult multi-timescale decision problem, we design a novel stochastic average gradient (SAG) based distributed algorithm and develop a push-pull augmented graph approach to prove its exact convergence at a linear rate of $\mathcal{O}(c^k)$ where $c\in(0,1)$ and $k$ increases by one no matter on which node updates. Finally, numerical experiments validate that our method speeds up linearly with respect to the number of nodes, and is robust to straggler nodes.

cs.LG↗

arXiv2020

POLY-HOOT: Monte-Carlo Planning in Continuous Space MDPs with Non-Asymptotic Analysis

Monte-Carlo planning, as exemplified by Monte-Carlo Tree Search (MCTS), has demonstrated remarkable performance in applications with finite spaces. In this paper, we consider Monte-Carlo planning in an environment with continuous state-action spaces, a much less understood problem with important applications in control and robotics. We introduce POLY-HOOT, an algorithm that augments MCTS with a continuous armed bandit strategy named Hierarchical Optimistic Optimization (HOO) (Bubeck et al., 2011). Specifically, we enhance HOO by using an appropriate polynomial, rather than logarithmic, bonus term in the upper confidence bounds. Such a polynomial bonus is motivated by its empirical successes in AlphaGo Zero (Silver et al., 2017b), as well as its significant role in achieving theoretical guarantees of finite space MCTS (Shah et al., 2019). We investigate, for the first time, the regret of the enhanced HOO algorithm in non-stationary bandit problems. Using this result as a building block, we establish non-asymptotic convergence guarantees for POLY-HOOT: the value estimate converges to an arbitrarily small neighborhood of the optimal value function at a polynomial rate. We further provide experimental results that corroborate our theoretical findings.

cs.AI↗

arXiv2020

Finite-Sample Analysis For Decentralized Batch Multi-Agent Reinforcement Learning With Networked Agents

Despite the increasing interest in multi-agent reinforcement learning (MARL) in multiple communities, understanding its theoretical foundation has long been recognized as a challenging problem. In this work, we address this problem by providing a finite-sample analysis for decentralized batch MARL with networked agents. Specifically, we consider two decentralized MARL settings, where teams of agents are connected by time-varying communication networks, and either collaborate or compete in a zero-sum game setting, without any central controller. These settings cover many conventional MARL settings in the literature. For both settings, we develop batch MARL algorithms that can be implemented in a decentralized fashion, and quantify the finite-sample errors of the estimated action-value functions. Our error analysis captures how the function class, the number of samples within each iteration, and the number of iterations determine the statistical accuracy of the proposed algorithms. Our results, compared to the finite-sample bounds for single-agent RL, involve additional error terms caused by decentralized computation, which is inherent in our decentralized MARL setting. This work appears to be the first finite-sample analysis for batch MARL, a step towards rigorous theoretical understanding of general MARL algorithms in the finite-sample regime.

cs.LG↗

arXiv2020

Reinforcement Learning in Non-Stationary Discrete-Time Linear-Quadratic Mean-Field Games

In this paper, we study large population multi-agent reinforcement learning (RL) in the context of discrete-time linear-quadratic mean-field games (LQ-MFGs). Our setting differs from most existing work on RL for MFGs, in that we consider a non-stationary MFG over an infinite horizon. We propose an actor-critic algorithm to iteratively compute the mean-field equilibrium (MFE) of the LQ-MFG. There are two primary challenges: i) the non-stationarity of the MFG induces a linear-quadratic tracking problem, which requires solving a backwards-in-time (non-causal) equation that cannot be solved by standard (causal) RL algorithms; ii) Many RL algorithms assume that the states are sampled from the stationary distribution of a Markov chain (MC), that is, the chain is already mixed, an assumption that is not satisfied for real data sources. We first identify that the mean-field trajectory follows linear dynamics, allowing the problem to be reformulated as a linear quadratic Gaussian problem. Under this reformulation, we propose an actor-critic algorithm that allows samples to be drawn from an unmixed MC. Finite-sample convergence guarantees for the algorithm are then provided. To characterize the performance of our algorithm in multi-agent RL, we have developed an error bound with respect to the Nash equilibrium of the finite-population game.

eess.SY↗

arXiv2020

Information State Embedding in Partially Observable Cooperative Multi-Agent Reinforcement Learning

Multi-agent reinforcement learning (MARL) under partial observability has long been considered challenging, primarily due to the requirement for each agent to maintain a belief over all other agents' local histories -- a domain that generally grows exponentially over time. In this work, we investigate a partially observable MARL problem in which agents are cooperative. To enable the development of tractable algorithms, we introduce the concept of an information state embedding that serves to compress agents' histories. We quantify how the compression error influences the resulting value functions for decentralized control. Furthermore, we propose an instance of the embedding based on recurrent neural networks (RNNs). The embedding is then used as an approximate information state, and can be fed into any MARL algorithm. The proposed embed-then-learn pipeline opens the black-box of existing (partially observable) MARL algorithms, allowing us to establish some theoretical guarantees (error bounds of value functions) while still achieving competitive performance with many end-to-end approaches.

cs.AI↗

arXiv2020

Global Convergence of Policy Gradient Methods to (Almost) Locally Optimal Policies

Policy gradient (PG) methods are a widely used reinforcement learning methodology in many applications such as video games, autonomous driving, and robotics. In spite of its empirical success, a rigorous understanding of the global convergence of PG methods is lacking in the literature. In this work, we close the gap by viewing PG methods from a nonconvex optimization perspective. In particular, we propose a new variant of PG methods for infinite-horizon problems that uses a random rollout horizon for the Monte-Carlo estimation of the policy gradient. This method then yields an unbiased estimate of the policy gradient with bounded variance, which enables the tools from nonconvex optimization to be applied to establish global convergence. Employing this perspective, we first recover the convergence results with rates to the stationary-point policies in the literature. More interestingly, motivated by advances in nonconvex optimization, we modify the proposed PG method by introducing periodically enlarged stepsizes. The modified algorithm is shown to escape saddle points under mild assumptions on the reward and the policy parameterization. Under a further strict saddle points assumption, this result establishes convergence to essentially locally-optimal policies of the underlying problem, and thus bridges the gap in existing literature on the convergence of PG methods. Results from experiments on the inverted pendulum are then provided to corroborate our theory, namely, by slightly reshaping the reward function to satisfy our assumption, unfavorable saddle points can be avoided and better limit points can be attained. Intriguingly, this empirical finding justifies the benefit of reward-reshaping from a nonconvex optimization perspective.

math.OC↗

arXiv2020

Approximate Equilibrium Computation for Discrete-Time Linear-Quadratic Mean-Field Games

While the topic of mean-field games (MFGs) has a relatively long history, heretofore there has been limited work concerning algorithms for the computation of equilibrium control policies. In this paper, we develop a computable policy iteration algorithm for approximating the mean-field equilibrium in linear-quadratic MFGs with discounted cost. Given the mean-field, each agent faces a linear-quadratic tracking problem, the solution of which involves a dynamical system evolving in retrograde time. This makes the development of forward-in-time algorithm updates challenging. By identifying a structural property of the mean-field update operator, namely that it preserves sequences of a particular form, we develop a forward-in-time equilibrium computation algorithm. Bounds that quantify the accuracy of the computed mean-field equilibrium as a function of the algorithm's stopping condition are provided. The optimality of the computed equilibrium is validated numerically. In contrast to the most recent/concurrent results, our algorithm appears to be the first to study infinite-horizon MFGs with non-stationary mean-field equilibria, though with focus on the linear quadratic setting.

eess.SY↗

arXiv2020

Non-Cooperative Inverse Reinforcement Learning

Making decisions in the presence of a strategic opponent requires one to take into account the opponent's ability to actively mask its intended objective. To describe such strategic situations, we introduce the non-cooperative inverse reinforcement learning (N-CIRL) formalism. The N-CIRL formalism consists of two agents with completely misaligned objectives, where only one of the agents knows the true objective function. Formally, we model the N-CIRL formalism as a zero-sum Markov game with one-sided incomplete information. Through interacting with the more informed player, the less informed player attempts to both infer, and act according to, the true objective function. As a result of the one-sided incomplete information, the multi-stage game can be decomposed into a sequence of single-stage games expressed by a recursive formula. Solving this recursive formula yields the value of the N-CIRL game and the more informed player's equilibrium strategy. Another recursive formula, constructed by forming an auxiliary game, termed the dual game, yields the less informed player's strategy. Building upon these two recursive formulas, we develop a computationally tractable algorithm to approximately solve for the equilibrium strategies. Finally, we demonstrate the benefits of our N-CIRL formalism over the existing multi-agent IRL formalism via extensive numerical simulation in a novel cyber security setting.

cs.GT↗

arXiv2019

Decentralized Multi-Agent Reinforcement Learning with Networked Agents: Recent Advances

Multi-agent reinforcement learning (MARL) has long been a significant and everlasting research topic in both machine learning and control. With the recent development of (single-agent) deep RL, there is a resurgence of interests in developing new MARL algorithms, especially those that are backed by theoretical analysis. In this paper, we review some recent advances a sub-area of this topic: decentralized MARL with networked agents. Specifically, multiple agents perform sequential decision-making in a common environment, without the coordination of any central controller. Instead, the agents are allowed to exchange information with their neighbors over a communication network. Such a setting finds broad applications in the control and operation of robots, unmanned vehicles, mobile sensor networks, and smart grid. This review is built upon several our research endeavors in this direction, together with some progresses made by other researchers along the line. We hope this review to inspire the devotion of more research efforts to this exciting yet challenging area.

cs.LG↗