Subgame solving without common knowledge

TL;DR

This paper presents a novel subgame solving method for imperfect-information games that reduces complexity by focusing on low-order knowledge, enabling practical application in complex games like dark chess.

Contribution

It introduces a low-order knowledge approach to subgame solving, overcoming the limitations of common-knowledge closure in complex imperfect-information games.

Findings

Reduced exploitability in practical games.

Enabled strong AI for dark chess.

Maintained safety guarantees with additional methods.

Abstract

In imperfect-information games, subgame solving is significantly more challenging than in perfect-information games, but in the last few years, such techniques have been developed. They were the key ingredient to the milestone of superhuman play in no-limit Texas hold'em poker. Current subgame-solving techniques analyze the entire common-knowledge closure of the player's current information set, that is, the smallest set of nodes within which it is common knowledge that the current node lies. While this is acceptable in games like poker where the common-knowledge closure is relatively small, many practical games have more complex information structure, which renders the common-knowledge closure impractically large to enumerate or even reasonably approximate. We introduce an approach that overcomes this obstacle, by instead working with only low-order knowledge. Our approach allows an agent, upon arriving at an infoset, to basically prune any node that is no longer reachable, thereby massively reducing the game tree size relative to the common-knowledge subgame. We prove that, as is, our approach can increase exploitability compared to the blueprint strategy. However, we develop three avenues by which safety can be guaranteed. Even without the safety-guaranteeing additions, experiments on medium-sized games show that our approach always reduced exploitability in practical games even when applied at every infoset, and a depth-limited version of it led to -- to our knowledge -- the first strong AI for the challenge problem dark chess.