A Generic Strategy Improvement Method for Simple Stochastic Games - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2021

A Generic Strategy Improvement Method for Simple Stochastic Games

Résumé

We present a generic strategy improvement algorithm (GSIA) to find an optimal strategy of simple stochastic games (SSG). We prove the correctness of GSIA, and derive a general complexity bound, which implies and improves on the results of several articles. First, we remove the assumption that the SSG is stopping, which is usually obtained by a polynomial blowup of the game. Second, we prove a tight bound on the denominator of the values associated to a strategy, and use it to prove that all strategy improvement algorithms are in fact fixed parameter tractable in the number r of random vertices. All known strategy improvement algorithms can be seen as instances of GSIA, which allows to analyze the complexity of converge from below by Condon [14] and to propose a class of algorithms generalising Gimbert and Horn's algorithm [16, 17]. These algorithms terminate in at most r! iterations, and for binary SSGs, they do less iterations than the current best deterministic algorithm given by Ibsen-Jensen and Miltersen [18].
Fichier non déposé

Dates et versions

hal-03401817 , version 1 (25-10-2021)

Licence

Paternité

Identifiants

Citer

David Auger, Xavier Badin De Montjoye, Yann Strozecki. A Generic Strategy Improvement Method for Simple Stochastic Games. 46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021, Aug 2021, Tallinn, Estonia. ⟨10.4230/LIPIcs.MFCS.2021.12⟩. ⟨hal-03401817⟩
44 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More