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On the Use of Non-Stationary Strategies for Solving Two-Player Zero-Sum Markov Games

Julien Pérolat 1, 2, 3 Bilal Piot 1, 2, 3 Bruno Scherrer 4, 5 Olivier Pietquin 3, 1, 6, 2
Abstract : The main contribution of this paper consists in extending several non-stationary Reinforcement Learning (RL) algorithms and their theoretical guarantees to the case of discounted zero-sum Markov Games (MGs).As in the case of Markov Decision Processes (MDPs), non-stationary algorithms are shown to exhibit better performance bounds compared to their stationary counterparts. The obtained bounds are generically composed of three terms: 1) a dependency over gamma (discount factor), 2) a concentrability coefficient and 3) a propagation error term. This error, depending on the algorithm, can be caused by a regression step, a policy evaluation step or a best-response evaluation step. As a second contribution, we empirically demonstrate, on generic MGs (called Garnets), that non-stationary algorithms outperform their stationary counterparts. In addition, it is shown that their performance mostly depends on the nature of the propagation error. Indeed, algorithms where the error is due to the evaluation of a best-response are penalized (even if they exhibit better concentrability coefficients and dependencies on gamma) compared to those suffering from a regression error.
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Contributor : Olivier Pietquin Connect in order to contact the contributor
Submitted on : Monday, March 21, 2016 - 3:39:13 PM
Last modification on : Thursday, January 20, 2022 - 4:17:17 PM


  • HAL Id : hal-01291495, version 1


Julien Pérolat, Bilal Piot, Bruno Scherrer, Olivier Pietquin. On the Use of Non-Stationary Strategies for Solving Two-Player Zero-Sum Markov Games. 19th International Conference on Artificial Intelligence and Statistics (AISTATS 2016), May 2016, Cadiz, Spain. ⟨hal-01291495⟩



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