用约束模型替代概率推断，让博弈代理更高效决策
Modeling Uncertainty: Constraint-Based Belief States in Imperfect-Information Games
- 用约束满足问题构建信念状态，避免复杂概率推导
- 在两种游戏中表现与概率方法几乎持平，性能差异极小
- 适合需快速推理的不完美信息博弈场景
在不完美信息博弈中，智能体需基于部分状态信息做决策。信念随机博弈模型通过将状态估计交由游戏模型自身处理，使智能体可直接使用外部提供的信念状态，从而减少对特定游戏的推理逻辑依赖。本文研究了两种表示隐藏棋子身份信念的方法：一种是基于约束满足问题的约束模型，另一种是利用信念传播估计边缘概率的概率扩展。我们在两个不同游戏中，使用通用智能体评估了两种表示方式的影响。结果表明，约束型信念的表现与概率推断相当，智能体性能差异微小。这说明在许多场景下，仅使用约束型信念状态即可实现有效决策。
原文摘要 · Abstract (English)
In imperfect-information games, agents must make decisions based on partial knowledge of the game state. The Belief Stochastic Game model addresses this challenge by delegating state estimation to the game model itself. This allows agents to operate on externally provided belief states, thereby reducing the need for game-specific inference logic. This paper investigates two approaches to represent beliefs in games with hidden piece identities: a constraint-based model using Constraint Satisfaction Problems and a probabilistic extension using Belief Propagation to estimate marginal probabilities. We evaluated the impact of both representations using general-purpose agents across two different games. Our findings indicate that constraint-based beliefs yield results comparable to those of probabilistic inference, with minimal differences in agent performance. This suggests that constraint-based belief states alone may suffice for effective decision-making in many settings.
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