Universal Decision Learners
This work provides a foundational mathematical framework for unifying diverse decision-making theories, which could benefit researchers in AI and machine learning by offering a common language and tools.
This paper proposes a Universal Decision Learner (UDL) as a common categorical formulation for various decision-making theories, extending partially specified decision functors from observed to new contexts using universal constructions. It demonstrates how Bellman equations, planning recursions, causal interventions, online regret, and equilibria emerge as special cases of this framework.
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.