# FP-IRL: Fokker--Planck Inverse Reinforcement Learning -- A Physics-Constrained Approach to Markov Decision Processes

arXiv: https://arxiv.org/abs/2306.10407 · HTML: https://mlsanity.com/paper/2306.10407/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse reinforcement learning, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 17 Jun 2023.

## Placed in

- Offline RL and imitation learning from data / [Inverse reinforcement learning](https://mlsanity.com/offlinerl/inverse-reinforcement-learning/)

## Builds on (most cited first, 9 of 9)

- [Guided Cost Learning: Deep Inverse Optimal Control via Policy Optimization](https://mlsanity.com/paper/1603.00448/) (2016)
- [A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progress](https://mlsanity.com/paper/1806.06877/) (2018)
- [IQ-Learn: Inverse soft-Q Learning for Imitation](https://mlsanity.com/paper/2106.12142/) (2021)
- [Multi-Agent Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1907.13220/) (2019)
- [OptionGAN: Learning Joint Reward-Policy Options using Generative Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1709.06683/) (2017)
- [Misspecification in Inverse Reinforcement Learning](https://mlsanity.com/paper/2212.03201/) (2022)
- [When Demonstrations Meet Generative World Models: A Maximum Likelihood Framework for Offline Inverse Reinforcement Learning](https://mlsanity.com/paper/2302.07457/) (2023)
- [Inverse Reinforcement Learning with Simultaneous Estimation of Rewards and Dynamics](https://mlsanity.com/paper/1604.03912/) (2016)
- [Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated data](https://mlsanity.com/paper/2001.04816/) (2020)

## Abstract (arXiv)

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 textita 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 that can be described 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 correspondence between MDPs and the FP equation, linking reward maximization in MDPs with free energy minimization in FP dynamics. This connection enables inference of the FP potential function using our inference approach of variational system identification, from which the full set of MDP components -- reward, transition, and policy -- can be recovered using analytic expressions. We demonstrate the effectiveness of FP-IRL through experiments on synthetic benchmarks and a modified version of the Mountain Car problem. Our results show that FP-IRL achieves accurate recovery of agent incentives while preserving computational efficiency and physical interpretability.