2 Search Results for "Zielonka, Wieslaw"

Document
DOI: 10.4230/LIPIcs.CONCUR.2020.24
Games Where You Can Play Optimally with Arena-Independent Finite Memory

Authors: Patricia Bouyer, Stéphane Le Roux, Youssouf Oualhadj, Mickael Randour, and Pierre Vandenhove

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
For decades, two-player (antagonistic) games on graphs have been a framework of choice for many important problems in theoretical computer science. A notorious one is controller synthesis, which can be rephrased through the game-theoretic metaphor as the quest for a winning strategy of the system in a game against its antagonistic environment. Depending on the specification, optimal strategies might be simple or quite complex, for example having to use (possibly infinite) memory. Hence, research strives to understand which settings allow for simple strategies. In 2005, Gimbert and Zielonka [Hugo Gimbert and Wieslaw Zielonka, 2005] provided a complete characterization of preference relations (a formal framework to model specifications and game objectives) that admit memoryless optimal strategies for both players. In the last fifteen years however, practical applications have driven the community toward games with complex or multiple objectives, where memory - finite or infinite - is almost always required. Despite much effort, the exact frontiers of the class of preference relations that admit finite-memory optimal strategies still elude us. In this work, we establish a complete characterization of preference relations that admit optimal strategies using arena-independent finite memory, generalizing the work of Gimbert and Zielonka to the finite-memory case. We also prove an equivalent to their celebrated corollary of great practical interest: if both players have optimal (arena-independent-)finite-memory strategies in all one-player games, then it is also the case in all two-player games. Finally, we pinpoint the boundaries of our results with regard to the literature: our work completely covers the case of arena-independent memory (e.g., multiple parity objectives, lower- and upper-bounded energy objectives), and paves the way to the arena-dependent case (e.g., multiple lower-bounded energy objectives).
Cite as

Patricia Bouyer, Stéphane Le Roux, Youssouf Oualhadj, Mickael Randour, and Pierre Vandenhove. Games Where You Can Play Optimally with Arena-Independent Finite Memory. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 24:1-24:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bouyer_et_al:LIPIcs.CONCUR.2020.24,
  author =	{Bouyer, Patricia and Le Roux, St\'{e}phane and Oualhadj, Youssouf and Randour, Mickael and Vandenhove, Pierre},
  title =	{{Games Where You Can Play Optimally with Arena-Independent Finite Memory}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{24:1--24:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.24},
  URN =		{urn:nbn:de:0030-drops-128360},
  doi =		{10.4230/LIPIcs.CONCUR.2020.24},
  annote =	{Keywords: two-player games on graphs, finite-memory determinacy, optimal strategies}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2010.65
Playing in stochastic environment: from multi-armed bandits to two-player games

Authors: Wieslaw Zielonka

Published in: LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)

Abstract
Given a zero-sum infinite game we examine the question if players have optimal memoryless deterministic strategies. It turns out that under some general conditions the problem for two-player games can be reduced to the same problem for one-player games which in turn can be reduced to a simpler related problem for multi-armed bandits.
Cite as

Wieslaw Zielonka. Playing in stochastic environment: from multi-armed bandits to two-player games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 65-72, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{zielonka:LIPIcs.FSTTCS.2010.65,
  author =	{Zielonka, Wieslaw},
  title =	{{Playing in stochastic environment: from multi-armed bandits to two-player games}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{65--72},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-23-1},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{8},
  editor =	{Lodaya, Kamal and Mahajan, Meena},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.65},
  URN =		{urn:nbn:de:0030-drops-28500},
  doi =		{10.4230/LIPIcs.FSTTCS.2010.65},
  annote =	{Keywords: two-player zero-sum game, one-player zero-sum game, multi-armed bandit, memoryless deterministic strategy}
}
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