ICS 2011

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Innovations in Computer Science - ICS 2011, Tsinghua University, Beijing, China, January 7-9, 2011. Proceedings, 253-263, 978-7-302-24517-9
Tsinghua University Press

Strategy iteration is strongly polynomial for 2-player turn-based stochastic games with a constant discount factor Authors : Thomas Dueholm Hansen, Peter Bro Miltersen, Uri Zwick [Download PDF]

Abstract:
Ye showed recently that the simplex method with Dantzig pivoting rule, as well as Howard's policy iteration algorithm, solve discounted Markov decision processes (MDPs), with a constant discount factor, in strongly polynomial time. More precisely, Ye showed that both algorithms terminate after at most О iterations, where n is the number of states, m is the total number of actions in the MDP, and 0 < γ < 1 is the discount factor. We improve Ye's analysis in two respects. First, we improve the bound given by Ye and show that Howard's policy iteration algorithm actually terminates after at most О iterations. Second, and more importantly, we show that the same bound applies to the number of iterations performed by the strategy iteration (or strategy improvement) algorithm, a generalization of Howard's policy iteration algorithm used for solving 2-player turn-based stochastic games with discounted zero-sum rewards. This provides the first strongly polynomial algorithm for solving these games, resolving a long standing open problem.

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