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Register a new userSolving Simple Stochastic Games with Few Random Vertices
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Hugo Gimbert
Publication date
2009
fields
Informatics Engineering
and research's language is
English
Authors
Hugo Gimbert
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Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them rely on the existence of optimal permutation strategies, a class of positional strategies derived from permutations of the random vertices. The permutation-enumeration algorithm performs an exhaustive search among these strategies, while the permutation-improvement algorithm is based on successive improvements, `a la Hoffman-Karp. Our algorithms improve previously known algorithms in several aspects. First they run in polynomial time when the number of random vertices is fixed, so the problem of solving simple stochastic games is fixed-parameter tractable when the parameter is the number of random vertices. Furthermore, our algorithms do not require the input game to be transformed into a stopping game. Finally, the permutation-enumeration algorithm does not use linear programming, while the permutation-improvement algorithm may run in polynomial time.
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Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three known classes of algorithms -- value iteration, strategy iteration and quadratic programming -- both theoretically and practically. Further, we suggest several improvements for all algorithms, including the first approach based on quadratic programming that avoids transforming the stochastic game to a stopping one. Our extensive experiments show that these improvements can lead to significant speed-ups. We implemented all algorithms in PRISM-games 3.0, thereby providing the first implementation of quadratic programming for solving simple stochastic games.
Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three known classes of algorithms -- value iteration, strategy iteration and quadratic programming -- both theoretically and practically. Further, we suggest several improvements for all algorithms, including the first approach based on quadratic programming that avoids transforming the stochastic game to a stopping one. Our extensive experiments show that these improvements can lead to significant speed-ups. We implemented all algorithms in PRISM-games 3.0, thereby providing the first implementation of quadratic programming for solving simple stochastic games.
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