Provably Efficient Off-Policy Adversarial Imitation Learning with Convergence Guarantees

Adversarial imitation learning (AIL) achieves high-quality imitation compared to behavioral cloning (BC), but demands substantial online environment interaction. Recent empirical work has explored initializing AIL algorithms with BC pretrained policies to address this limitation, yet a rigorous theoretical understanding of pretraining's role in AIL remains elusive. This paper provides a systematic theoretical analysis and introduces principled pretraining algorithms for accelerating AIL. We begin by analyzing AIL with policy pretraining alone, identifying reward error as the dominant source of suboptimality. This reveals a critical and previously overlooked gap: the absence of reward pretraining. Motivated by this finding, we develop a principled policy-reward co-pretraining approach grounded in a reward shaping analysis. Our analysis uncovers a fundamental connection between expert policies and shaping rewards, which naturally gives rise to CoPT-AIL, an approach that jointly pretrains both policy and reward through a single BC procedure. We prove that CoPT-AIL achieves an improved imitation gap bound over standard AIL, establishing the first theoretical guarantee for the benefits of pretraining in AIL. Experimental results confirm CoPT-AIL's superior performance over existing AIL methods.

Adversarial imitation learning (AIL), a prominent approach in imitation learning, has achieved significant practical success powered by neural network approximation. However, existing theoretical analyses of AIL are primarily confined to simplified settings, such as tabular and linear function approximation, and involve complex algorithmic designs that impede practical implementation. This creates a substantial gap between theory and practice. This paper bridges this gap by exploring the theoretical underpinnings of online AIL with general function approximation. We introduce a novel framework called optimization-based AIL (OPT-AIL), which performs online optimization for reward learning coupled with optimism-regularized optimization for policy learning. Within this framework, we develop two concrete methods: model-free OPT-AIL and model-based OPT-AIL. Our theoretical analysis demonstrates that both variants achieve polynomial expert sample complexity and interaction complexity for learning near-expert policies. To the best of our knowledge, they represent the first provably efficient AIL methods under general function approximation. From a practical standpoint, OPT-AIL requires only the approximate optimization of two objectives, thereby facilitating practical implementation. Empirical studies demonstrate that OPT-AIL outperforms previous state-of-the-art deep AIL methods across several challenging tasks.

In this paper, we establish last-iterate convergence rates for off-policy actor--critic methods in reinforcement learning. In particular, under a single-loop, single-timescale implementation and a broad class of policy updates, including approximate policy iteration and natural policy gradient methods, we prove the first $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity guarantee for finding an $ε$-optimal policy under minimal assumptions, namely, the existence of a policy that induces an irreducible Markov chain. This stands in stark contrast to the existing literature, where an $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity is achieved only through nested-loop updates and/or under strong, algorithm-dependent assumptions on the policies, such as uniform mixing and uniform exploration. Technically, to address the challenges posed by the coupled update equations arising from the single-loop implementation, as well as the potentially unbounded iterates induced by off-policy learning, our analysis is based on a coupled Lyapunov drift framework. Specifically, we establish a geometric convergence rate for the actor and an $\tilde{\mathcal{O}}(1/T)$ convergence rate for the critic, and combine the two Lyapunov drift inequalities through a cross-domination property. We believe this analytical framework is of independent interest and may be applicable to other coupled iterative algorithms with unbounded