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Reinforcement Learning as (Discrete) Potential Theory
arXiv:2608.17181v1 Announce Type: new Abstract: Reinforcement learning (RL) theory fundamentally depends on probability theory through the Markov chain. There is a deep connection between probability
arXiv:2608.17181v1 Announce Type: new 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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Source: arXiv cs.LG | 2026-08-19