Solving Irreducible Stochastic Mean-Payoff Games and Entropy Games by Relative Krasnoselskii-Mann Iteration - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2023

Solving Irreducible Stochastic Mean-Payoff Games and Entropy Games by Relative Krasnoselskii-Mann Iteration

Marianne Akian
  • Function : Author
Stéphane Gaubert

Abstract

We analyse an algorithm solving stochastic mean-payoff games, combining the ideas of relative value iteration and of Krasnoselskii-Mann damping. We derive parameterized complexity bounds for several classes of games satisfying irreducibility conditions. We show in particular that an ε-approximation of the value of an irreducible concurrent stochastic game can be computed in a number of iterations in O(|log(ε)|) where the constant in the O(⋅) is explicit, depending on the smallest non-zero transition probabilities. This should be compared with a bound in O(ε^{-1}|log(ε)|) obtained by Chatterjee and Ibsen-Jensen (ICALP 2014) for the same class of games, and to a O(ε^{-1}) bound by Allamigeon, Gaubert, Katz and Skomra (ICALP 2022) for turn-based games. We also establish parameterized complexity bounds for entropy games, a class of matrix multiplication games introduced by Asarin, Cervelle, Degorre, Dima, Horn and Kozyakin. We derive these results by methods of variational analysis, establishing contraction properties of the relative Krasnoselskii-Mann iteration with respect to Hilbert’s semi-norm.

Dates and versions

hal-04365602 , version 1 (28-12-2023)

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Marianne Akian, Stéphane Gaubert, Ulysse Naepels, Basile Terver. Solving Irreducible Stochastic Mean-Payoff Games and Entropy Games by Relative Krasnoselskii-Mann Iteration. MFCS 2023 - 48th International Symposium on Mathematical Foundations of Computer Science, Aug 2023, Bordeaux, France. ⟨10.4230/LIPIcs.MFCS.2023.10⟩. ⟨hal-04365602⟩
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