@inproceedings{7583b6e812fb45f79c43192650a0c5e3,
title = "The operator approach to entropy games",
abstract = "Entropy games and matrix multiplication games have been recently introduced by Asarin et al. They model the situation in which one player (Despot) wishes to minimize the growth rate of a matrix product, whereas the other player (Tribune) wishes to maximize it. We develop an operator approach to entropy games. This allows us to show that entropy games can be cast as stochastic mean payoff games in which some action spaces are simplices and payments are given by a relative entropy (Kullback-Leibler divergence). In this way, we show that entropy games with a fixed number of states belonging to Despot can be solved in polynomial time. This approach also allows us to solve these games by a policy iteration algorithm, which we compare with the spectral simplex algorithm developed by Protasov.",
keywords = "Perron eigenvalues, Policy iteration, Risk sensitive control, Shapley operators, Stochastic games",
author = "Marianne Akian and St{\'e}phane Gaubert and Julien Grand-Cl{\'e}ment and J{\'e}r{\'e}mie Guillaud",
note = "Publisher Copyright: {\textcopyright} Marianne Akian, St{\'e}phane Gaubert, Julien Grand-Cl{\'e}ment, and J{\'e}r{\'e}mie Guillaud.; 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017 ; Conference date: 08-03-2017 Through 11-03-2017",
year = "2017",
month = mar,
day = "1",
doi = "10.4230/LIPIcs.STACS.2017.6",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Brigitte Vallee and Heribert Vollmer",
booktitle = "34th Symposium on Theoretical Aspects of Computer Science, STACS 2017",
}