Online Learning in Unknown Markov Games

Abstract

We study online learning in unknown Markov games, a problem that arises in episodic multi-agent reinforcement learning where the actions of the opponents are unobservable. We show that in this challenging setting, achieving sublinear regret against the best response in hindsight is statistically hard. We then consider a weaker notion of regret by competing with the \emph{minimax value} of the game, and present an algorithm that achieves a sublinear $\tilde{\mathcal{O}}(K^{2/3})$ regret after $K$ episodes. This is the first sublinear regret bound (to our knowledge) for online learning in unknown Markov games. Importantly, our regret bound is independent of the size of the opponents' action spaces. As a result, even when the opponents' actions are fully observable, our regret bound improves upon existing analysis (e.g., (Xie et al., 2020)) by an exponential factor in the number of opponents.

25 pages

References in corpus (10)

• Safe, Multi-Agent, Reinforcement Learning for Autonomous Driving
• Provably efficient RL with Rich Observations via Latent State Decoding
• Provable Self-Play Algorithms for Competitive Reinforcement Learning
• Online Convex Optimization in Adversarial Markov Decision Processes
• Almost Optimal Model-Free Reinforcement Learning via Reference-Advantage Decomposition
• Learning Adversarial MDPs with Bandit Feedback and Unknown Transition
• Solving Discounted Stochastic Two-Player Games with Near-Optimal Time and Sample Complexity
• Feature-Based Q-Learning for Two-Player Stochastic Games
• Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexity
• Near-Optimal Reinforcement Learning with Self-Play