# Balance Equation-based Distributionally Robust Offline Imitation Learning

arXiv: https://arxiv.org/abs/2511.07942 · HTML: https://mlsanity.com/paper/2511.07942/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

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

- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [A Generalist Agent](https://mlsanity.com/paper/2205.06175/) (2022)
- [Sim-to-Real Transfer of Robotic Control with Dynamics Randomization](https://mlsanity.com/paper/1710.06537/) (2017)
- [One-Shot Visual Imitation Learning via Meta-Learning](https://mlsanity.com/paper/1709.04905/) (2017)
- [DART: Noise Injection for Robust Imitation Learning](https://mlsanity.com/paper/1703.09327/) (2017)
- [Imitation Learning via Off-Policy Distribution Matching](https://mlsanity.com/paper/1912.05032/) (2019)
- [One-Shot Imitation from Observing Humans via Domain-Adaptive Meta-Learning](https://mlsanity.com/paper/1802.01557/) (2018)
- [Imitation Learning from Imperfect Demonstration](https://mlsanity.com/paper/1901.09387/) (2019)
- [Robust Reinforcement Learning using Offline Data](https://mlsanity.com/paper/2208.05129/) (2022)
- [Task-Embedded Control Networks for Few-Shot Imitation Learning](https://mlsanity.com/paper/1810.03237/) (2018)
- [Generalization in Dexterous Manipulation via Geometry-Aware Multi-Task Learning](https://mlsanity.com/paper/2111.03062/) (2021)
- [Cross-domain Imitation from Observations](https://mlsanity.com/paper/2105.10037/) (2021)
- [Distributional Robustness and Regularization in Reinforcement Learning](https://mlsanity.com/paper/2003.02894/) (2020)
- [Robust Inverse Reinforcement Learning under Transition Dynamics Mismatch](https://mlsanity.com/paper/2007.01174/) (2020)
- [Watch, Try, Learn: Meta-Learning from Demonstrations and Reward](https://mlsanity.com/paper/1906.03352/) (2019)
- [Robust Imitation Learning from Noisy Demonstrations](https://mlsanity.com/paper/2010.10181/) (2020)
- [Robust Imitation Learning against Variations in Environment Dynamics](https://mlsanity.com/paper/2206.09314/) (2022)
- [IntervenGen: Interventional Data Generation for Robust and Data-Efficient Robot Imitation Learning](https://mlsanity.com/paper/2405.01472/) (2024)
- [ODRL: A Benchmark for Off-Dynamics Reinforcement Learning](https://mlsanity.com/paper/2410.20750/) (2024)
- [ODICE: Revealing the Mystery of Distribution Correction Estimation via Orthogonal-gradient Update](https://mlsanity.com/paper/2402.00348/) (2024)
- [Bridging Distributionally Robust Learning and Offline RL: An Approach to Mitigate Distribution Shift and Partial Data Coverage](https://mlsanity.com/paper/2310.18434/) (2023)
- [Rethinking Latent Redundancy in Behavior Cloning: An Information Bottleneck Approach for Robot Manipulation](https://mlsanity.com/paper/2502.02853/) (2025)
- [Contact-Implicit Model Predictive Control for Dexterous In-hand Manipulation: A Long-Horizon and Robust Approach](https://mlsanity.com/paper/2402.18897/) (2024)
- [ADAIL: Adaptive Adversarial Imitation Learning](https://mlsanity.com/paper/2008.12647/) (2020)
- [Markov Balance Satisfaction Improves Performance in Strictly Batch Offline Imitation Learning](https://mlsanity.com/paper/2408.09125/) (2024)
- [Conditional Kernel Imitation Learning for Continuous State Environments](https://mlsanity.com/paper/2308.12573/) (2023)
- [Robust Behavior Cloning Via Global Lipschitz Regularization](https://mlsanity.com/paper/2506.19250/) (2025)

## Built on by (most cited first, 1 of 1)

- [When Dynamics Shift, Robust Task Inference Wins: Offline Imitation Learning with Behavior Foundation Models Revisited](https://mlsanity.com/paper/2605.17017/) (2026)

## Abstract (arXiv)

Imitation Learning (IL) has proven highly effective for robotic and control tasks where manually designing reward functions or explicit controllers is infeasible. However, standard IL methods implicitly assume that the environment dynamics remain fixed between training and deployment. In practice, this assumption rarely holds where modeling inaccuracies, real-world parameter variations, and adversarial perturbations can all induce shifts in transition dynamics, leading to severe performance degradation. We address this challenge through Balance Equation-based Distributionally Robust Offline Imitation Learning, a framework that learns robust policies solely from expert demonstrations collected under nominal dynamics, without requiring further environment interaction. We formulate the problem as a distributionally robust optimization over an uncertainty set of transition models, seeking a policy that minimizes the imitation loss under the worst-case transition distribution. Importantly, we show that this robust objective can be reformulated entirely in terms of the nominal data distribution, enabling tractable offline learning. Empirical evaluations on continuous-control benchmarks demonstrate that our approach achieves superior robustness and generalization compared to state-of-the-art offline IL baselines, particularly under perturbed or shifted environments.