FP-IRL: Fokker-planck Inverse Reinforcement Learning -- A Physics-constrained Approach To Markov Decision Processes

Abstract

Inverse reinforcement learning (IRL) is a powerful paradigm for uncovering the incentive structure that drives agent behavior, by inferring an unknown reward function from observed trajectories within a Markov decision process (MDP). However, most existing IRL methods require access to the transition function, either prescribed or estimated \textit\{a priori\}, which poses significant challenges when the underlying dynamics are unknown, unobservable, or not easily sampled. We propose Fokker--Planck inverse reinforcement learning (FP-IRL), a novel physics-constrained IRL framework tailored for systems governed by Fokker--Planck (FP) dynamics. FP-IRL simultaneously infers both the reward and transition functions directly from trajectory data, without requiring access to sampled transitions. Our method leverages a conjectured equivalence between MDPs and the FP equation, linking reward maximization in MDPs with free energy minimization in FP dynamics. This connection enables inference o

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