A Sharp Analysis of Model-based Reinforcement Learning with Self-Play

Qinghua Liu, Tiancheng Yu, Yu Bai, Chi Jin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

43 Scopus citations


Model-based algorithms-algorithms that explore the environment through building and utilizing an estimated model-are widely used in reinforcement learning practice and theoretically shown to achieve optimal sample efficiency for single-agent reinforcement learning in Markov Decision Processes (MDPs). However, for multi-agent reinforcement learning in Markov games, the current best known sample complexity for model-based algorithms is rather suboptimal and compares unfavorably against recent model-free approaches. In this paper, we present a sharp analysis of model-based self-play algorithms for multi-agent Markov games. We design an algorithm Optimistic Nash Value Iteration (Nash-VI) for two-player zero-sum Markov games that is able to output an ∊-approximate Nash policy in Õ(H3SAB/∊2) episodes of game playing, where S is the number of states, A, B are the number of actions for the two players respectively, and H is the horizon length. This significantly improves over the best known model-based guarantee of Õ(H4S2AB/∊2), and is the first that matches the information-theoretic lower bound Ω(H3S(A + B)/∊2) except for a min {A, B} factor. In addition, our guarantee compares favorably against the best known model-free algorithm if min {A, B} = o(H3), and outputs a single Markov policy while existing sample-efficient model-free algorithms output a nested mixture of Markov policies that is in general non-Markov and rather inconvenient to store and execute. We further adapt our analysis to designing a provably efficient task-agnostic algorithm for zero-sum Markov games, and designing the first line of provably sample-efficient algorithms for multi-player general-sum Markov games.

Original languageEnglish (US)
Title of host publicationProceedings of the 38th International Conference on Machine Learning, ICML 2021
PublisherML Research Press
Number of pages10
ISBN (Electronic)9781713845065
StatePublished - 2021
Event38th International Conference on Machine Learning, ICML 2021 - Virtual, Online
Duration: Jul 18 2021Jul 24 2021

Publication series

NameProceedings of Machine Learning Research
ISSN (Electronic)2640-3498


Conference38th International Conference on Machine Learning, ICML 2021
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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