论文提出结构化马尔可夫决策过程决策边界的几何理论

研究建立了政策诱导决策几何的结构性质，引入了边界和决策复杂性的内在概念，并获得了从黑盒政策查询中估计边界和重建政策的统计保证。

A Geometric Theory of Decision Boundaries in Structured Markov Decision Processes

Classical dynamic programming represents optimal sequential decisions through value functions and policies. While this functional representation is natural for computing optimal decisions, it does not directly identify the mathematical object governing policy reconstruction, representation complexity, or oracle-query complexity once an optimal policy is fixed. This paper addresses this question by developing a geometric theory of structured optimal policies in which the decision-boundary geometry induced by the policy becomes the primary object of analysis. We show that, under suitable structural regularity conditions, this geometry provides the minimal representation required for policy reconstruction and determines the statistical and computational complexity of the reconstruction problem. Building upon this representation, we establish structural properties of policy-induced decision geometry, introduce intrinsic notions of boundary and decision complexity, derive information-theoretic measures of decision compression, and obtain statistical guarantees for boundary estimation and policy reconstruction from black-box policy queries. Collectively, these results demonstrate that, for the structured decision problems considered here, the complexity of policy reconstruction is governed by the geometry of the decision boundary rather than by the cardinality of the ambient state space. Controlled numerical experiments examine the principal theoretical predictions and provide empirical evidence consistent with the proposed framework.

本条情报归属 AITOP「论文」核心栏目，重点聚焦北美前沿实验室与硅谷科技巨头。在跨区域产业观察坐标中，该动态直接关联「AI 开发者工具链、Coding Agent 与工程化实践」研究主线，反映出当前技术演进与商业落地的最新风向。涉及核心实体与技术议题包括：Geometric Theory of Decision Boundaries、Structured Markov Decision Processes、决策边界、马尔可夫决策过程，读者可通过下方标签进入对应专题页查阅历史脉络与关联对比。

信源核验说明：本文原始线索采编自「arXiv cs.LG」（@Fredy Pokou），经 AITOP 多维评分管线结构化提炼。