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Model-Free Reinforcement Learning for Stochastic Parity Games

Authors Ernst Moritz Hahn , Mateo Perez , Sven Schewe , Fabio Somenzi , Ashutosh Trivedi , Dominik Wojtczak

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Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Computing methodologies → Machine learning algorithms
  • Mathematics of computing → Markov processes
  • Theory of computation → Convergence and learning in games
Keywords
  • Reinforcement learning
  • Stochastic games
  • Omega-regular objectives

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Abstract

This paper investigates the use of model-free reinforcement learning to compute the optimal value in two-player stochastic games with parity objectives. In this setting, two decision makers, player Min and player Max, compete on a finite game arena - a stochastic game graph with unknown but fixed probability distributions - to minimize and maximize, respectively, the probability of satisfying a parity objective. We give a reduction from stochastic parity games to a family of stochastic reachability games with a parameter ε, such that the value of a stochastic parity game equals the limit of the values of the corresponding simple stochastic games as the parameter ε tends to 0. Since this reduction does not require the knowledge of the probabilistic transition structure of the underlying game arena, model-free reinforcement learning algorithms, such as minimax Q-learning, can be used to approximate the value and mutual best-response strategies for both players in the underlying stochastic parity game. We also present a streamlined reduction from 1 1/2-player parity games to reachability games that avoids recourse to nondeterminism. Finally, we report on the experimental evaluations of both reductions.

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Ernst Moritz Hahn, Mateo Perez, Sven Schewe, Fabio Somenzi, Ashutosh Trivedi, and Dominik Wojtczak. Model-Free Reinforcement Learning for Stochastic Parity Games. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.CONCUR.2020.21

Author Details

Ernst Moritz Hahn
  • University of Twente, Enschede, The Netherlands
Mateo Perez
  • University of Colorado Boulder, CO, USA
Sven Schewe
  • University of Liverpool, UK
Fabio Somenzi
  • University of Colorado Boulder, CO, USA
Ashutosh Trivedi
  • University of Colorado Boulder, CO, USA
Dominik Wojtczak
  • University of Liverpool, UK

Funding

This work has been supported by the National Natural Science Foundation of China (Grant Nr. 61532019), by the Engineering and Physical Sciences Research Council grants EP/M027287/1 and EP/P020909/1, by a CU Boulder Research and Innovation Office grant, and by the National Science Foundation grant 2009022.

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