KrwEmd: Revising the Imperfect-Recall Abstraction from Forgetting Everything

TL;DR

The paper tackles excessive abstraction in hand abstraction for large imperfect-information games by revisiting imperfect-recall and introducing history-aware features. It develops KrwEmd, which combines k-recall winrate Isomorphism with Earth Mover’s Distance to cluster signal observation infosets, enabling adaptable, history-informed abstractions within the SOOG framework. Through Numeral211 Hold’em experiments, KrwEmd consistently outperforms prior methods such as PAOI, EHS, and PAAEMD, demonstrating the value of incorporating historical information, especially in late phases. The approach offers practical improvements for poker AI and suggests directions for scalable, history-aware abstraction in complex IIGs, with future work on distributed computation and alternative clustering methods.

Abstract

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.

Figures (4)

• Figure 1: In a 3-phase hand abstraction task for games, the objective is to group hands A and B—they share the same future trajectory despite following distinct historical paths (consistent information is represented by paths of the same color). However, when an imperfect-recall abstraction that entirely discards historical information is adopted, both hands are assigned identical features.
• Figure 2: The hand ranks of Numeral211 hold'em.
• Figure 3: The isomorphism frameworks experiment was trained for $5.5\times 10^{10}$ iterations, with (a) representing the symmetric abstraction setting and (b) representing the asymmetric abstraction setting. Both instances of KrwEmd outperform PAOI, while the performance of 2-RWI and 2-ROI shows almost no difference in the Numeral211 environment.
• Figure 4: Performance comparison of KrwEmd versus other imperfect-recall signal observation abstraction algorithms considering only future information, trained for $3.7 \times 10^{10}$ iterations. All instances of KrwEmd outperform the benchmark, and comparisons between KrwEmd instances indicate that late-game information is more important than early-game information.

Theorems & Definitions (4)

• Definition 1: Imperfect-Information Game (IIG)
• Definition 2: Signal Observation Ordered Game (SOOG)
• Proposition 1
• proof