# Distributional Inverse Reinforcement Learning

arXiv: https://arxiv.org/abs/2510.03013 · HTML: https://mlsanity.com/paper/2510.03013/

## 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 39 of its 75 references that are in the map.
- First posted on arXiv 3 Oct 2025.

## Placed in

- Offline RL and imitation learning from data / [Inverse reinforcement learning](https://mlsanity.com/offlinerl/inverse-reinforcement-learning/)
- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 30 of 39)

- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [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)
- [Imitation Learning via Off-Policy Distribution Matching](https://mlsanity.com/paper/1912.05032/) (2019)
- [Maximum Entropy Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/1507.04888/) (2015)
- [Distributional Soft Actor-Critic: Off-Policy Reinforcement Learning for Addressing Value Estimation Errors](https://mlsanity.com/paper/2001.02811/) (2020)
- [f-IRL: Inverse Reinforcement Learning via State Marginal Matching](https://mlsanity.com/paper/2011.04709/) (2020)
- [Risk-Averse Offline Reinforcement Learning](https://mlsanity.com/paper/2102.05371/) (2021)
- [Scalable Bayesian Inverse Reinforcement Learning](https://mlsanity.com/paper/2102.06483/) (2021)
- [Maximum-Likelihood Inverse Reinforcement Learning with Finite-Time Guarantees](https://mlsanity.com/paper/2210.01808/) (2022)
- [Efficient Sampling-Based Maximum Entropy Inverse Reinforcement Learning with Application to Autonomous Driving](https://mlsanity.com/paper/2006.13704/) (2020)
- [Robust Inverse Reinforcement Learning under Transition Dynamics Mismatch](https://mlsanity.com/paper/2007.01174/) (2020)
- [Driving with Style: Inverse Reinforcement Learning in General-Purpose Planning for Automated Driving](https://mlsanity.com/paper/1905.00229/) (2019)
- [When Demonstrations Meet Generative World Models: A Maximum Likelihood Framework for Offline Inverse Reinforcement Learning](https://mlsanity.com/paper/2302.07457/) (2023)
- [Foundations of Multivariate Distributional Reinforcement Learning](https://mlsanity.com/paper/2409.00328/) (2024)
- [Risk-Sensitive Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1808.04468/) (2018)
- [Diffusing States and Matching Scores: A New Framework for Imitation Learning](https://mlsanity.com/paper/2410.13855/) (2024)
- [Internally Rewarded Reinforcement Learning](https://mlsanity.com/paper/2302.00270/) (2023)
- [Learning Risk-Aware Quadrupedal Locomotion using Distributional Reinforcement Learning](https://mlsanity.com/paper/2309.14246/) (2023)
- [A Primer on Maximum Causal Entropy Inverse Reinforcement Learning](https://mlsanity.com/paper/2203.11409/) (2022)
- [Risk-sensitive Inverse Reinforcement Learning via Semi- and Non-Parametric Methods](https://mlsanity.com/paper/1711.10055/) (2017)
- [A Bayesian Approach to Robust Inverse Reinforcement Learning](https://mlsanity.com/paper/2309.08571/) (2023)
- [Inverse Reinforcement Learning with the Average Reward Criterion](https://mlsanity.com/paper/2305.14608/) (2023)

## Abstract (arXiv)

We propose a distributional framework for offline Inverse Reinforcement Learning (IRL) that jointly models uncertainty over reward functions and full distributions of returns. Unlike conventional IRL approaches that recover a deterministic reward estimate or match only expected returns, our method captures richer structure in expert behavior, particularly in learning the reward distribution, by minimizing first-order stochastic dominance (FSD) violations and thus integrating distortion risk measures (DRMs) into policy learning, enabling the recovery of both reward distributions and distribution-aware policies. This formulation is well-suited for behavior analysis and risk-aware imitation learning. Theoretical analysis shows that the algorithm converges with O(varepsilon-2) iteration complexity. Empirical results on synthetic benchmarks, real-world neurobehavioral data, and MuJoCo control tasks demonstrate that our method recovers expressive reward representations and achieves state-of-the-art performance.