学习如何以指数级更少的空间搜索规划方案

中文摘要 AI 辅助

即使启发式算法近乎完美，用于规划的启发式搜索也可能存储指数级多的状态。我们转而学习搜索控制，每个领域对应一个规范，该规范被编写为索引策略：一种带有寄存器（用于存储对象）和模式（用于对规则进行排序）的广义策略。我们添加了选择规则，该规则将对象加载到寄存器中并标记回溯点，其中一个候选对象就足够；其他所有规则必须适用于其所有结果，且无需搜索。我们的主要结果是，结构终止性（排除无限执行）还将每次执行的时间限制为对象数量的多项式。随后，深度优先过程可在多项式空间内找到规划方案，无论状态空间多大，都无需使用已访问状态列表。代价是时间仅在选择深度（执行过程中实际选择的数量）上呈指数级增长。因此，此类策略解决的任何类别都属于NP问题，且在选择深度为常数时属于P问题。我们通过语言模型在反例引导的循环中学习这些策略，该循环可验证终止性、验证训练任务并保持选择深度较小。使用所学策略，该过程解决了IPC 2023学习赛道和Autoscale Agile套件的1890个测试任务中的1709个，超过了LAMA、BFWS和Levitron，且其中大多数任务在1秒和100 MiB内完成。

英文摘要

Heuristic search for a plan can store exponentially many states, even when its heuristic is almost perfect. We instead learn search control, one specification per domain, written as an indexical policy: a generalized policy with registers that hold objects and modes that sequence its rules. We add the choose rule, which loads an object into a register and marks a backtracking point, where one candidate suffices; every other rule must work for all of its outcomes and needs no search. Our main result is that structural termination, which rules out infinite executions, also bounds every execution by a polynomial in the number of objects. A depth-first procedure then finds a plan in polynomial space, however large the state space, with no list of visited states. The cost is time, exponential only in the choice depth, the number of real choices along an execution. Any class that such a policy solves therefore lies in NP, and in P at constant choice depth. We learn these policies with a language model in a counterexample-guided loop that certifies termination, verifies the training tasks, and keeps the choice depth small. With the learned policies, the procedure solves 1,709 of 1,890 test tasks of the IPC 2023 Learning Track and the Autoscale Agile suite, more than LAMA, BFWS, and Levitron, and most of them within one second and 100 MiB.

发表机构

• Linköping University（林雪平大学）
• RWTH Aachen University（亚琛工业大学）
• Universidad Simón Bolívar（西蒙玻利瓦尔大学）

机构由 AI 辅助整理，请以论文原文为准。