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Sound Search in Imperfect Information Games | | Michal Šustr
; Martin Schmid
; Matej Moravčík
; Neil Burch
; Marc Lanctot
; Michael Bowling
; | | Date: |
15 Jun 2020 | | Abstract: | Search has played a fundamental role in computer game research since the very
beginning. And while online search has been commonly used in perfect
information games such as Chess and Go, online search methods for imperfect
information games have only been introduced relatively recently. This paper
addresses the question of what is sound search in an imperfect information
setting of two-player zero-sum games? We argue that the fixed-strategy
definitions of exploitability and epsilon-Nash equilibria are ill suited to
measure the worst-case performance of an online search algorithm. We thus
formalize epsilon-soundness, a concept that connects the worst-case performance
of an online algorithm to the performance of an epsilon-Nash equilibrium. As
epsilon-soundness can be difficult to compute in general, we also introduce a
consistency framework -- a hierarchy that connects the behavior of an online
algorithm to a Nash equilibrium. Our multiple levels of consistency describe in
what sense an online algorithm plays ’’just like a fixed Nash equilibrium’’.
These notions further illustrate the difference in perfect and imperfect
information settings, as the same consistency guarantees have different
worst-case online performance in perfect and imperfect information games. Our
definition of soundness and the consistency hierarchy finally provide
appropriate tools to analyze online algorithms in imperfect information games.
We thus inspect some of the previous online algorithms in a new light, bringing
new insights into their worst case performance guarantees. | | Source: | arXiv, 2006.8740 | | Services: | Forum | Review | PDF | Favorites | |
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