Year: 2022
Type: preprint
Abstract: Multi-Agent Reinforcement Learning (MARL) -- where multiple agents learn to interact in a shared dynamic environment -- permeates across a wide range of critical applications. While there has been substantial progress on understanding the global convergence of policy optimization methods in single-agent RL, designing and analysis of efficient policy optimization algorithms in the MARL setting present significant challenges, which unfortunately, remain highly inadequately addressed by existing theory. In this paper, we focus on the most basic setting of competitive multi-agent RL, namely two-player zero-sum Markov games, and study equilibrium finding algorithms in both the infinite-horizon discounted setting and the finite-horizon episodic setting. We propose a single-loop policy optimization method with symmetric updates from both agents, where the policy is updated via the entropy-regularized optimistic multiplicative weights update (OMWU) method and the value is updated on a slower timescale. We show that, in the full-information tabular setting, the proposed method achieves a finite-time last-iterate linear convergence to the quantal response equilibrium of the regularized problem, which translates to a sublinear last-iterate convergence to the Nash equilibrium by controlling the amount of regularization. Our convergence results improve upon the best known iteration complexities, and lead to a better understanding of policy optimization in competitive Markov games.
Source: arXiv (Cornell University)
Authors: Cen, Shicong, Chi, Yuejie, Du, Simon S., Xiao, Lin
Institution: Carnegie Mellon University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1469985387, RINGS: Learning-Enabled Ground and Air Integrated Networks (GAINs), CIF: Medium: Collaborative Research: Theory of Optimization Geometry and Algorithms for Neural Networks, IIS:RI Theoretical Foundations of Reinforcement Learning: From Tabula Rasa to Function Approximation, G4353487559, Collaborative Research: CIF: Medium: Statistical and Algorithmic Foundations of Efficient Reinforcement Learning, CAREER: Toward a Foundation of Over-Parameterization, G5972442391, Collaborative Research: SCALE MoDL: Adaptivity of Deep Neural Networks, Collaborative Research: CIF: Medium: MoDL:Toward a Mathematical Foundation of Deep Reinforcement Learning, AI Institute: Institute for Foundations of Machine Learning, G8876996369
OpenAlex ID: W4302013128