DeepAI AI Chat
Log In Sign Up

The operator approach to entropy games

04/10/2019
by   Marianne Akian, et al.
Inria
Ecole Polytechnique
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/17/2022

Universal Complexity Bounds Based on Value Iteration and Application to Entropy Games

We develop value iteration-based algorithms to solve in a unified manner...
03/05/2023

Uncoupled and Convergent Learning in Two-Player Zero-Sum Markov Games

We revisit the problem of learning in two-player zero-sum Markov games, ...
10/14/2021

On the ESL algorithm for solving energy games

We propose a variant of an algorithm introduced by Schewe and also studi...
09/13/2019

Controlling a Random Population is EXPTIME-hard

Bertrand et al. [1] (LMCS 2019) describe two-player zero-sum games in wh...
04/08/2022

The Complexity of Infinite-Horizon General-Sum Stochastic Games

We study the complexity of computing stationary Nash equilibrium (NE) in...
02/14/2017

Entropy Non-increasing Games for the Improvement of Dataflow Programming

In this article, we introduce a new conception of a family of esport gam...
11/28/2021

On Thermodynamic Interpretation of Copula Entropy

Copula Entropy (CE) is a recently introduced concept for measuring corre...