The operator approach to entropy games

Marianne Akian 1 Stéphane Gaubert 1 Julien Grand-Clément 2 Jérémie Guillaud 3
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
3 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, MINES ParisTech - École nationale supérieure des mines de Paris, SU - Sorbonne Université, Inria de Paris
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.
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Submitted on : Wednesday, May 29, 2019 - 3:53:43 PM
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Marianne Akian, Stéphane Gaubert, Julien Grand-Clément, Jérémie Guillaud. The operator approach to entropy games. Theory of Computing Systems, Springer Verlag, In press, ⟨10.1007/s00224-019-09925-z⟩. ⟨hal-02143807⟩



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