Policy iteration for perfect information stochastic mean payoff games with bounded first return times is strongly polynomial

Abstract

Recent results of Ye and Hansen, Miltersen and Zwick show that policy iteration for one or two player (perfect information) zero-sum stochastic games, restricted to instances with a fixed discount rate, is strongly polynomial. We show that policy iteration for mean-payoff zero-sum stochastic games is also strongly polynomial when restricted to instances with bounded first mean return time to a given state. The proof is based on methods of nonlinear Perron-Frobenius theory, allowing us to reduce the mean-payoff problem to a discounted problem with state dependent discount rate. Our analysis also shows that policy iteration remains strongly polynomial for discounted problems in which the discount rate can be state dependent (and even negative) at certain states, provided that the spectral radii of the nonnegative matrices associated to all strategies are bounded from above by a fixed constant strictly less than 1.

17 pages

References in corpus (2)

• Strategy iteration is strongly polynomial for 2-player turn-based stochastic games with a constant discount factor
• Policy iteration algorithm for zero-sum multichain stochastic games with mean payoff and perfect information

Cited by in corpus (3)

• Geometric Policy Iteration for Markov Decision Processes
• Solving Ergodic Markov Decision Processes and Perfect Information Zero-sum Stochastic Games by Variance Reduced Deflated Value Iteration
• Reduction of total-cost and average-cost MDPs with weakly continuous transition probabilities to discounted MDPs