Near-Optimal Second-Order Guarantees for Model-Based Adversarial Imitation Learning
This work addresses the theoretical gaps in understanding online interaction and stochasticity in imitation learning, providing foundational insights for the field.
The paper tackles the problem of online adversarial imitation learning by introducing a model-based algorithm (MB-AIL) that achieves horizon-free, second-order sample-complexity guarantees, scaling with policy variance and matching minimax-optimal bounds up to logarithmic factors.
We study online adversarial imitation learning (AIL), where an agent learns from offline expert demonstrations and interacts with the environment online without access to rewards. Despite strong empirical results, the benefits of online interaction and the impact of stochasticity remain poorly understood. We address these gaps by introducing a model-based AIL algorithm (MB-AIL) and establish its horizon-free, second-order sample-complexity guarantees under general function approximations for both expert data and reward-free interactions. These second-order bounds provide an instance-dependent result that can scale with the variance of returns under the relevant policies and therefore tighten as the system approaches determinism. Together with second-order, information-theoretic lower bounds on a newly constructed hard-instance family, we show that MB-AIL attains minimax-optimal sample complexity for online interaction (up to logarithmic factors) with limited expert demonstrations and matches the lower bound for expert demonstrations in terms of the dependence on horizon $H$, precision $ε$ and the policy variance $σ^2$. Experiments further validate our theoretical findings and demonstrate that a practical implementation of MB-AIL matches or surpasses the sample efficiency of existing methods.