Universal Decision Learners

2026-05-28

AI Summary

This study addresses the challenge of coherently extending local decision-making information into globally consistent behavioral policies across diverse paradigms, including planning, reinforcement learning, causal intervention, online learning, and game-theoretic equilibria. To this end, the authors propose the Universal Decision Learner (UDL) framework, which—drawing on category theory for the first time in this context—employs left and right Kan extensions to uniformly extend local decision functors to novel situations. The work establishes Kan-invariant notions of behavioral equivalence and minimal abstraction, revealing a shared universal extension principle underlying various decision-making approaches. By leveraging universal properties, it formally unifies major decision theories as special cases of UDL and demonstrates its practical efficacy through successful instantiation in reinforcement learning settings.

Abstract

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.

Problem

• decision making
• universal construction
• Kan extension
• behavioral coherence
• context extension

Innovation

• Universal Decision Learner
• Kan extension
• categorical decision theory
• behavioral equivalence
• universal construction