# Reinforcement Learning as (Discrete) Potential Theory

arXiv: https://arxiv.org/abs/2608.17181 · HTML: https://mlsanity.com/paper/2608.17181/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 0 of its 15 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Abstract (arXiv)

Reinforcement learning (RL) theory fundamentally depends on probability theory through the Markov chain. There is a deep connection between probability theory and potential theory. This paper reviews that connection and explores the potential-theoretic viewpoint for core reinforcement learning representations and algorithms under a fixed-policy assumption. This viewpoint may offer a path for improved sample efficiency and formal constraints that can be applied to RL. When the fixed-policy assumption is relaxed, the linear potential theory framework can be naturally extended to the nonlinear case.