No-Regret Strategy Solving in Imperfect-Information Games via Pre-Trained Embedding

High-quality information set abstraction remains a core challenge in solving large-scale imperfect-information extensive-form games (IIEFGs)-such as no-limit Texas Hold'em-where the finite nature of spatial resources hinders strategy solving over the full game. State-of-the-art AI methods rely on pre-trained discrete clustering for abstraction, yet their hard classification irreversibly loses critical information: specifically, the quantifiable subtle differences between information sets-vital for strategy solving-thereby compromising the quality of such solving. Inspired by the word embedding paradigm in natural language processing, this paper proposes the Embedding CFR algorithm, a novel approach for solving strategies in IIEFGs within an embedding space. The algorithm pre-trains and embeds features of isolated information sets into an interconnected low-dimensional continuous space, where the resulting vectors more precisely capture both the distinctions and connections between information sets. Embedding CFR presents a strategy-solving process driven by regret accumulation and strategy updates within this embedding space, with accompanying theoretical analysis verifying its capacity to reduce cumulative regret. Experiments on poker show that with the same spatial overhead, Embedding CFR achieves significantly faster exploitability convergence compared to cluster-based abstraction algorithms, confirming its effectiveness. Furthermore, to our knowledge, it is the first algorithm in poker AI that pre-trains information set abstractions through low-dimensional embedding for strategy solving.

KrwEmd: Revising the Imperfect-Recall Abstraction from Forgetting Everything

Excessive abstraction is a critical challenge in hand abstraction-a task specific to games like Texas hold'em-when solving large-scale imperfect-information games, as it impairs AI performance. This issue arises from extreme implementations of imperfect-recall abstraction, which entirely discard historical information. This paper presents KrwEmd, the first practical algorithm designed to address this problem. We first introduce the k-recall winrate feature, which not only qualitatively distinguishes signal observation infosets by leveraging both future and, crucially, historical game information, but also quantitatively captures their similarity. We then develop the KrwEmd algorithm, which clusters signal observation infosets using earth mover's distance to measure discrepancies between their features. Experimental results demonstrate that KrwEmd significantly improves AI gameplay performance compared to existing algorithms.