Tight Performance Guarantees of Imitator Policies with Continuous Actions
This work addresses a theoretical gap for researchers in imitation learning, providing foundational insights but is incremental as it extends existing finite-action analysis to continuous settings.
The paper tackles the lack of theoretical guarantees for Behavioral Cloning with continuous actions by deriving a performance bound based on Wasserstein distance under Lipschitz assumptions, and shows that noise injection can strengthen these guarantees at the cost of bias.
Behavioral Cloning (BC) aims at learning a policy that mimics the behavior demonstrated by an expert. The current theoretical understanding of BC is limited to the case of finite actions. In this paper, we study BC with the goal of providing theoretical guarantees on the performance of the imitator policy in the case of continuous actions. We start by deriving a novel bound on the performance gap based on Wasserstein distance, applicable for continuous-action experts, holding under the assumption that the value function is Lipschitz continuous. Since this latter condition is hardy fulfilled in practice, even for Lipschitz Markov Decision Processes and policies, we propose a relaxed setting, proving that value function is always Holder continuous. This result is of independent interest and allows obtaining in BC a general bound for the performance of the imitator policy. Finally, we analyze noise injection, a common practice in which the expert action is executed in the environment after the application of a noise kernel. We show that this practice allows deriving stronger performance guarantees, at the price of a bias due to the noise addition.