# Markov Balance Satisfaction Improves Performance in Strictly Batch Offline Imitation Learning

arXiv: https://arxiv.org/abs/2408.09125 · HTML: https://mlsanity.com/paper/2408.09125/

## Key facts

- Cited by 3 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 27 of its 49 references that are in the map.
- First posted on arXiv 17 Aug 2024.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progress](https://mlsanity.com/paper/1806.06877/) (2018)
- [Discriminator-Actor-Critic: Addressing Sample Inefficiency and Reward Bias in Adversarial Imitation Learning](https://mlsanity.com/paper/1809.02925/) (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)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Imitation Learning as f-Divergence Minimization](https://mlsanity.com/paper/1905.12888/) (2019)
- [Discriminator-Weighted Offline Imitation Learning from Suboptimal Demonstrations](https://mlsanity.com/paper/2207.10050/) (2022)
- [Off-Policy Imitation Learning from Observations](https://mlsanity.com/paper/2102.13185/) (2021)
- [Scalable Bayesian Inverse Reinforcement Learning](https://mlsanity.com/paper/2102.06483/) (2021)
- [Strictly Batch Imitation Learning by Energy-based Distribution Matching](https://mlsanity.com/paper/2006.14154/) (2020)
- [Versatile Offline Imitation from Observations and Examples via Regularized State-Occupancy Matching](https://mlsanity.com/paper/2202.02433/) (2022)
- [Truly Batch Apprenticeship Learning with Deep Successor Features](https://mlsanity.com/paper/1903.10077/) (2019)
- [Mitigating Covariate Shift in Imitation Learning via Offline Data Without Great Coverage](https://mlsanity.com/paper/2106.03207/) (2021)
- [Gaussian Process Conditional Density Estimation](https://mlsanity.com/paper/1810.12750/) (2018)
- [ODICE: Revealing the Mystery of Distribution Correction Estimation via Orthogonal-gradient Update](https://mlsanity.com/paper/2402.00348/) (2024)
- [On the Universality of Volume-Preserving and Coupling-Based Normalizing Flows](https://mlsanity.com/paper/2402.06578/) (2024)
- [SoftDICE for Imitation Learning: Rethinking Off-policy Distribution Matching](https://mlsanity.com/paper/2106.03155/) (2021)
- [A Critique of Strictly Batch Imitation Learning](https://mlsanity.com/paper/2110.02063/) (2021)

## Built on by (most cited first, 3 of 3)

- [Balance Equation-based Distributionally Robust Offline Imitation Learning](https://mlsanity.com/paper/2511.07942/) (2025)
- [When Dynamics Shift, Robust Task Inference Wins: Offline Imitation Learning with Behavior Foundation Models Revisited](https://mlsanity.com/paper/2605.17017/) (2026)
- [Expert Behavior Prior Reinforcement Learning](https://mlsanity.com/paper/2607.21302/) (2026)

## Abstract (arXiv)

Imitation learning (IL) is notably effective for robotic tasks where directly programming behaviors or defining optimal control costs is challenging. In this work, we address a scenario where the imitator relies solely on observed behavior and cannot make environmental interactions during learning. It does not have additional supplementary datasets beyond the expert's dataset nor any information about the transition dynamics. Unlike state-of-the-art (SOTA) IL methods, this approach tackles the limitations of conventional IL by operating in a more constrained and realistic setting. Our method uses the Markov balance equation and introduces a novel conditional density estimation-based imitation learning framework. It employs conditional normalizing flows for transition dynamics estimation and aims at satisfying a balance equation for the environment. Through a series of numerical experiments on Classic Control and MuJoCo environments, we demonstrate consistently superior empirical performance compared to many SOTA IL algorithms.