# Provable Benefits of Regularization: Fast Rates for Adversarial Imitation Learning

arXiv: https://arxiv.org/abs/2609.35698 · HTML: https://mlsanity.com/paper/2609.35698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 20 of its 28 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [IQ-Learn: Inverse soft-Q Learning for Imitation](https://mlsanity.com/paper/2106.12142/) (2021)
- [Toward the Fundamental Limits of Imitation Learning](https://mlsanity.com/paper/2009.05990/) (2020)
- [Provably Efficient Imitation Learning from Observation Alone](https://mlsanity.com/paper/1905.10948/) (2019)
- [Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning](https://mlsanity.com/paper/2407.15007/) (2024)
- [What Matters for Adversarial Imitation Learning?](https://mlsanity.com/paper/2106.00672/) (2021)
- [Fast Rates for Maximum Entropy Exploration](https://mlsanity.com/paper/2303.08059/) (2023)
- [Online Apprenticeship Learning](https://mlsanity.com/paper/2102.06924/) (2021)
- [LS-IQ: Implicit Reward Regularization for Inverse Reinforcement Learning](https://mlsanity.com/paper/2303.00599/) (2023)
- [Provably Efficient Adversarial Imitation Learning with Unknown Transitions](https://mlsanity.com/paper/2306.06563/) (2023)
- [Imitation Learning in Discounted Linear MDPs without exploration assumptions](https://mlsanity.com/paper/2405.02181/) (2024)
- [Achieving Logarithmic Regret in KL-Regularized Zero-Sum Markov Games](https://mlsanity.com/paper/2510.13060/) (2025)
- [A Nearly Optimal and Low-Switching Algorithm for Reinforcement Learning with General Function Approximation](https://mlsanity.com/paper/2311.15238/) (2023)
- [Provably Efficient Generative Adversarial Imitation Learning for Online and Offline Setting with Linear Function Approximation](https://mlsanity.com/paper/2108.08765/) (2021)
- [Demonstration-Regularized RL](https://mlsanity.com/paper/2310.17303/) (2023)
- [Provably and Practically Efficient Adversarial Imitation Learning with General Function Approximation](https://mlsanity.com/paper/2411.00610/) (2024)
- [Near-Optimal Second-Order Guarantees for Model-Based Adversarial Imitation Learning](https://mlsanity.com/paper/2510.09487/) (2025)
- [Fast Rates for Inverse Reinforcement Learning](https://mlsanity.com/paper/2605.14599/) (2026)

## Abstract (arXiv)

We study adversarial imitation learning (AIL), in which an agent learns to imitate expert demonstrations by optimizing a policy against an adversarial reward that distinguishes expert and learner behavior. Historically, reward regularization and entropy-based policy regularization are key components of empirically successful methods such as GAIL and LS-IQ, yet their finite-sample benefits remain underexplored. We establish fast rates for jointly regularized AIL in finite-horizon Markov decision processes with general function approximation. Our model-free algorithm, Dually Regularized AIL, combines KL policy regularization with a quadratic reward penalty weighted by expert and learner occupancies. With K online episodes and N expert trajectories, we prove a widetildeOleft(frac1K+frac1Nright) bound on the regularized imitation gap for fixed regularization parameters. Our analysis combines an online mirror descent construction for general convex reward classes to control estimation error from finite expert data and stochastic learner feedback, with a sharp analysis of optimistic KL-regularized policy learning. To the best of our knowledge, Dually Regularized AIL is the first algorithm to simultaneously achieve widetildeOleft(frac1εright) sample complexity in both expert demonstrations and online interactions for this regularized AIL objective, even with stochastic experts. These results provide a rigorous characterization of the complementary statistical benefits of reward and policy regularization in AIL.