Provably Efficient Offline Multi-agent Reinforcement Learning via Strategy-wise Bonus

• URL: http://arxiv.org/abs/2206.00159v1
• Date: Wed, 1 Jun 2022 00:18:15 GMT
• Title: Provably Efficient Offline Multi-agent Reinforcement Learning via Strategy-wise Bonus
• Authors: Qiwen Cui and Simon S. Du
• Abstract summary: We propose a strategy-wise concentration principle which builds a confidence interval for the joint strategy. For two-player zero-sum Markov games, by exploiting the convexity of the strategy-wise bonus, we propose an efficient algorithm. All of our algorithms can naturally take a pre-specified strategy class $Pi$ as input and output a strategy close to the best strategy in $Pi$.
• Score: 48.34563955829649
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper considers offline multi-agent reinforcement learning. We propose the strategy-wise concentration principle which directly builds a confidence interval for the joint strategy, in contrast to the point-wise concentration principle that builds a confidence interval for each point in the joint action space. For two-player zero-sum Markov games, by exploiting the convexity of the strategy-wise bonus, we propose a computationally efficient algorithm whose sample complexity enjoys a better dependency on the number of actions than the prior methods based on the point-wise bonus. Furthermore, for offline multi-agent general-sum Markov games, based on the strategy-wise bonus and a novel surrogate function, we give the first algorithm whose sample complexity only scales $\sum_{i=1}^mA_i$ where $A_i$ is the action size of the $i$-th player and $m$ is the number of players. In sharp contrast, the sample complexity of methods based on the point-wise bonus would scale with the size of the joint action space $\Pi_{i=1}^m A_i$ due to the curse of multiagents. Lastly, all of our algorithms can naturally take a pre-specified strategy class $\Pi$ as input and output a strategy that is close to the best strategy in $\Pi$. In this setting, the sample complexity only scales with $\log |\Pi|$ instead of $\sum_{i=1}^mA_i$.

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