# Universal Decision Learners

arXiv: https://arxiv.org/abs/2605.30694 · HTML: https://mlsanity.com/paper/2605.30694/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 2 of its 20 references that are in the map.
- First posted on arXiv 29 May 2026.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 2 of 2)

- [Online Vector Balancing and Geometric Discrepancy](https://mlsanity.com/paper/1912.03350/) (2019)
- [Universal Decision Models](https://mlsanity.com/paper/2110.15431/) (2021)

## Built on by (most cited first, 1 of 1)

- [Learning in Infinitesimal Non-Compositional Sketches](https://mlsanity.com/paper/2607.15107/) (2026)

## Abstract (arXiv)

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.