Provable Benefits of Regularization: Fast Rates for Adversarial Imitation Learning

Hanbin Zhou, Shangzhe Li, Alexander Braverman, Weitong Zhang

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 $\widetilde{O}\left(\frac{1}{K}+\frac{1}{N}\right)$ 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…