用范畴论统一多种决策模型，让局部行为自然扩展为全局一致决策。
Universal Decision Learners
- 基于左/右坎扩张构建通用决策学习框架
- 涵盖规划、强化学习、因果干预等多类决策问题
- 适合对决策理论与数学建模感兴趣的学者
许多决策理论——如规划、强化学习、因果干预、在线学习和博弈论均衡——都能将局部信息转化为全局一致的行为。本文提出一种统一的范畴论表述：通用决策学习器（UDL）通过一对普遍构造，将已观察上下文中的部分决策函子扩展到新上下文。左坎扩张表达展开、聚合与候选生成；右坎扩张表达一致性、约束满足与不动点语义。核心观点并非所有决策问题有相同算法，而是许多决策形式都可视为同一类普遍问题：以标准方式扩展局部行为数据，再刻画全局一致的扩展。本文给出抽象的UDL构造，证明其普遍比较性质，定义坎不变的行为等价与最小抽象，并展示贝尔曼方程、规划递归、因果干预、在线遗憾及均衡如何成为特例。附录进一步详述强化学习情形。
原文摘要 · Abstract (English)
Many theories of decision making -- planning, reinforcement learning, causal intervention, online learning, and game-theoretic equilibrium -- turn local information into globally coherent behavior. This paper proposes a common categorical formulation: a Universal Decision Learner (UDL) extends a partially specified decision functor from observed contexts to new contexts by a pair of universal constructions. Left Kan extensions express rollout, aggregation, and candidate generation; right Kan extensions express consistency, constraint satisfaction, and fixed-point semantics. The central claim is not that every decision problem has the same algorithm, but that many decision formalisms instantiate the same universal problem: extend local behavioral data canonically, then characterize the globally coherent extensions. We give the abstract UDL construction, prove its universal comparison property, define Kan-invariant behavioral equivalence and minimal abstractions, and show how Bellman equations, planning recursions, causal interventions, online regret, and equilibria arise as special cases. The supplementary material develops the reinforcement-learning specialization in more detail.
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