Decision making is a central problem in AI that can be formalized using a Markov Decision Process. A problem is that, with increasing numbers of (indistinguishable) objects, the state space grows exponentially. To compute policies, the state space has to be enumerated. Even more possibilities have to be enumerated if the size of the action space depends on the size of the state space, especially if we allow concurrent actions. To tackle the exponential blow-up in the action and state space, we present a first-order representation to store the spaces in polynomial instead of exponential size in the number of objects and introduce Foreplan, a relational forward planner, which uses this representation to efficiently compute policies for numerous indistinguishable objects and actions. Additionally, we introduce an even faster approximate version of Foreplan. Moreover, Foreplan identifies how many objects an agent should act on to achieve a certain task given restrictions. Further, we provide a theoretical analysis and an empirical evaluation of Foreplan, demonstrating a speedup of at least four orders of magnitude.

翻译：决策制定是人工智能中的一个核心问题，可通过马尔可夫决策过程进行形式化描述。一个关键挑战在于，随着（不可区分）对象数量的增加，状态空间呈指数级增长。为计算策略，必须枚举整个状态空间。若动作空间的规模依赖于状态空间的规模，尤其是在允许并发动作的情况下，需要枚举的可能性将进一步激增。为应对动作空间和状态空间的指数级爆炸问题，我们提出了一种一阶表示方法，以多项式而非指数级规模存储空间（相对于对象数量），并介绍了Foreplan——一种关系型前向规划器，它利用此表示高效计算涉及大量不可区分对象和动作的策略。此外，我们提出了Foreplan的一种更快速的近似版本。同时，Foreplan能够识别在给定约束条件下，智能体为完成特定任务应对多少对象执行动作。进一步，我们提供了Foreplan的理论分析和实证评估，证明其至少实现了四个数量级的加速。