Policy Evaluation and Seeking for Multi-Agent Reinforcement Learning via Best Response

• URL: http://arxiv.org/abs/2006.09585v2
• Date: Sat, 20 Jun 2020 04:22:47 GMT
• Title: Policy Evaluation and Seeking for Multi-Agent Reinforcement Learning via Best Response
• Authors: Rui Yan and Xiaoming Duan and Zongying Shi and Yisheng Zhong and Jason R. Marden and Francesco Bullo
• Abstract summary: We adopt strict best response dynamics to model selfish behaviors at a meta-level for multi-agent reinforcement learning. Our approach is more compatible with single-agent reinforcement learning than alpha-rank which relies on weakly better responses.
• Score: 15.149039407681945
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces two metrics (cycle-based and memory-based metrics), grounded on a dynamical game-theoretic solution concept called sink equilibrium, for the evaluation, ranking, and computation of policies in multi-agent learning. We adopt strict best response dynamics (SBRD) to model selfish behaviors at a meta-level for multi-agent reinforcement learning. Our approach can deal with dynamical cyclical behaviors (unlike approaches based on Nash equilibria and Elo ratings), and is more compatible with single-agent reinforcement learning than alpha-rank which relies on weakly better responses. We first consider settings where the difference between largest and second largest underlying metric has a known lower bound. With this knowledge we propose a class of perturbed SBRD with the following property: only policies with maximum metric are observed with nonzero probability for a broad class of stochastic games with finite memory. We then consider settings where the lower bound for the difference is unknown. For this setting, we propose a class of perturbed SBRD such that the metrics of the policies observed with nonzero probability differ from the optimal by any given tolerance. The proposed perturbed SBRD addresses the opponent-induced non-stationarity by fixing the strategies of others for the learning agent, and uses empirical game-theoretic analysis to estimate payoffs for each strategy profile obtained due to the perturbation.

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