Universal Decision Learners
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Computer Science > Machine Learning
Title:Universal Decision Learners
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.
| Comments: | 15 pages |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.30694 [cs.LG] |
| (or arXiv:2605.30694v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.30694
arXiv-issued DOI via DataCite (pending registration)
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