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arXiv · 1007.1812

The complexity of solving reachability games using value and strategy iteration

Kristoffer Arnsfelt Hansen·Rasmus Ibsen-Jensen·Peter Bro Miltersen
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Abstract

Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations needed by both of these algorithms for providing non-trivial approximations to the value of a game with N non-terminal positions and m actions for each player in each position. In particular, both algorithms have doubly-exponential complexity. Even when the game given as input has only one non-terminal position, we prove an exponential lower bound on the worst case number of iterations needed to provide non-trivial approximations.

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Kristoffer Arnsfelt Hansen, Rasmus Ibsen-Jensen, Peter Bro Miltersen. 2010-07-12. The complexity of solving reachability games using value and strategy iteration. https://arxiv.org/abs/1007.1812

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