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arXiv · 2608.17181

Reinforcement Learning as (Discrete) Potential Theory

Christopher Connolly
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Abstract

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.

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Christopher Connolly. 2026-08-17. Reinforcement Learning as (Discrete) Potential Theory. https://arxiv.org/abs/2608.17181

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