On Reinforcement Learning for Turn-based Zero-sum Markov Games
Name
3412815.3416888.pdf
Description
Published version
Size
1.28 MB
Format
Adobe PDF
Checksum (MD5)
c3c8340fe0562291cea7a9ffa342fc67
Author(s)
Shah, D
Somani, V
Xie, Q
Xu, Z
Date Issued
2020
Journal
FODS 2020 - Proceedings of the 2020 ACM-IMS Foundations of Data Science Conference
Publisher
ACM
Citation
Shah, D, Somani, V, Xie, Q and Xu, Z. 2020. "On Reinforcement Learning for Turn-based Zero-sum Markov Games." FODS 2020 - Proceedings of the 2020 ACM-IMS Foundations of Data Science Conference.
Version
Final published version
Abstract
© 2020 Owner/Author. We consider the problem of finding Nash equilibrium for two-player turn-based zero-sum games. Inspired by the AlphaGo Zero (AGZ) algorithm, we develop a Reinforcement Learning based approach. Specifically, we propose Explore-Improve-Supervise (EIS) method that combines "exploration", "policy improvement"and "supervised learning"to find the value function and policy associated with Nash equilibrium. We identify sufficient conditions for convergence and correctness for such an approach. For a concrete instance of EIS where random policy is used for "exploration", Monte-Carlo Tree Search is used for "policy improvement"and Nearest Neighbors is used for "supervised learning", we establish that this method finds an\varepsilon-approximate value function of Nash equilibrium in\widetildeO(\varepsilon^-(d+4)) steps when the underlying state-space of the game is continuous and d-dimensional. This is nearly optimal as we establish a lower bound of\widetildeØmega (\varepsilon^-(d+2)) for any policy.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3412815.3416888
