Comparison of algorithms for simple stochastic games
Simple stochastic games are turn-based 2½-player zero-sum graph games with a reachability objective. The problem is to compute the winning probabilities as well as the optimal strategies of both players. In this paper, we compare the three known classes of algorithms – value iteration, strategy iter...
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01.11.2022
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| Abstract | Simple stochastic games are turn-based 2½-player zero-sum graph games with a reachability objective. The problem is to compute the winning probabilities 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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| AbstractList | Simple stochastic games are turn-based 2½-player zero-sum graph games with a reachability objective. The problem is to compute the winning probabilities 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. |
| ArticleNumber | 104885 |
| Author | Weininger, Maximilian Ramneantu, Emanuel Křetínský, Jan Slivinskiy, Alexander |
| Author_xml | – sequence: 1 givenname: Jan surname: Křetínský fullname: Křetínský, Jan – sequence: 2 givenname: Emanuel surname: Ramneantu fullname: Ramneantu, Emanuel – sequence: 3 givenname: Alexander surname: Slivinskiy fullname: Slivinskiy, Alexander – sequence: 4 givenname: Maximilian orcidid: 0000-0002-0163-2152 surname: Weininger fullname: Weininger, Maximilian email: maximilian.weininger@tum.de |
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| Cites_doi | 10.1007/s10703-010-0097-6 10.1145/210332.210339 10.1002/9780470316887 10.1006/inco.1995.1035 10.1016/j.ejcon.2016.04.009 10.1016/j.entcs.2004.07.008 10.1007/s10703-013-0183-7 10.1016/0304-3975(95)00188-3 10.1007/s00453-010-9413-1 10.1137/0203021 10.1007/s00224-013-9524-6 10.1016/j.jcss.2012.12.001 10.4204/EPTCS.326.9 10.1016/j.jcss.2011.05.002 10.1287/mnsc.12.5.359 10.1016/j.tcs.2016.12.003 10.1016/0890-5401(92)90048-K 10.1016/0041-5553(80)90098-1 |
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| Keywords | Stochastic games Strategy iteration Algorithms Probabilistic verification Value iteration Formal methods Quadratic programming |
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