Uncoupled and Convergent Learning in Two-Player Zero-Sum Markov Games with Bandit Feedback

• URL: http://arxiv.org/abs/2303.02738v2
• Date: Wed, 8 Nov 2023 19:47:17 GMT
• Title: Uncoupled and Convergent Learning in Two-Player Zero-Sum Markov Games with Bandit Feedback
• Authors: Yang Cai, Haipeng Luo, Chen-Yu Wei, Weiqiang Zheng
• Abstract summary: We focus on developing an algorithm that is uncoupled, convergent, and rational, with non-asymptotic convergence rates. Our algorithm is related to [Chen et al., 2021, Cen et al., 2021] and also builds on the entropy regularization technique.
• Score: 49.1061436241109
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We revisit the problem of learning in two-player zero-sum Markov games, focusing on developing an algorithm that is uncoupled, convergent, and rational, with non-asymptotic convergence rates. We start from the case of stateless matrix game with bandit feedback as a warm-up, showing an $O(t^{-\frac{1}{8}})$ last-iterate convergence rate. To the best of our knowledge, this is the first result that obtains finite last-iterate convergence rate given access to only bandit feedback. We extend our result to the case of irreducible Markov games, providing a last-iterate convergence rate of $O(t^{-\frac{1}{9+\varepsilon}})$ for any $\varepsilon>0$. Finally, we study Markov games without any assumptions on the dynamics, and show a path convergence rate, which is a new notion of convergence we defined, of $O(t^{-\frac{1}{10}})$. Our algorithm removes the coordination and prior knowledge requirement of [Wei et al., 2021], which pursued the same goals as us for irreducible Markov games. Our algorithm is related to [Chen et al., 2021, Cen et al., 2021] and also builds on the entropy regularization technique. However, we remove their requirement of communications on the entropy values, making our algorithm entirely uncoupled.

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