arXiv:2510.15094cs.GTcs.AI2025-10被引 1

提出新框架提升扑克类游戏抽象精度,解决传统方法丢失历史信息的问题

Beyond Outcome-Based Imperfect-Recall: Higher-Resolution Abstractions for Imperfect-Information Games

  • 构建信号观测博弈模型,分离信号与行动序列,建立手牌抽象的数学基础
  • 证明主流方法因随意丢弃历史信息导致性能损失,且提出分辨率上限理论
  • 设计全历史保真同构机制,实验显示在德州扑克基准上持续超越基线

手牌抽象对扩展不完美信息博弈(如德州扑克)至关重要,但进展受限于缺乏正式任务模型以及依赖高资源策略求解的评估方式。本文提出信号观测有序博弈(SOOGs),一类专为德州风格游戏设计的子类,清晰分离信号与玩家行动序列,为手牌抽象提供精确的数学基础。在此框架中,我们定义分辨率边界——在给定信号抽象下可达到性能的信息论上限。利用该边界,我们证明主流基于结果的不完全回忆算法因任意丢弃历史信息而造成显著损失;通过潜在感知结果同构(PAOI)形式化此行为,并证明其刻画了这些算法的分辨率边界。为克服此局限,我们提出全回忆结果同构(FROI),整合历史信息以提升边界并改善策略质量。在德州扑克风格基准上的实验表明,FROI始终优于基于结果的不完全回忆基线。研究结果为手牌抽象提供了统一的正式处理方式,并为设计更高分辨率抽象提供了实用指导。

原文摘要 · Abstract (English)

Hand abstraction is crucial for scaling imperfect-information games (IIGs) such as Texas Hold'em, yet progress is limited by the lack of a formal task model and by evaluations that require resource-intensive strategy solving. We introduce signal observation ordered games (SOOGs), a subclass of IIGs tailored to hold'em-style games that cleanly separates signal from player action sequences, providing a precise mathematical foundation for hand abstraction. Within this framework, we define a resolution bound-an information-theoretic upper bound on achievable performance under a given signal abstraction. Using the bound, we show that mainstream outcome-based imperfect-recall algorithms suffer substantial losses by arbitrarily discarding historical information; we formalize this behavior via potential-aware outcome Isomorphism (PAOI) and prove that PAOI characterizes their resolution bound. To overcome this limitation, we propose full-recall outcome isomorphism (FROI), which integrates historical information to raise the bound and improve policy quality. Experiments on hold'em-style benchmarks confirm that FROI consistently outperforms outcome-based imperfect-recall baselines. Our results provide a unified formal treatment of hand abstraction and practical guidance for designing higher-resolution abstractions in IIGs.

博弈论扑克AI抽象机制

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