On the Sample Complexity of Stability Constrained Imitation Learning

We study the following question in the context of imitation learning for continuous control: how are the underlying stability properties of an expert policy reflected in the sample complexity of an imitation learning task? We provide the first results showing that a granular connection can be made between the expert system’s incremental gain stability, a novel measure of robust convergence between pairs of system trajectories, and the dependency on the task horizon T of the resulting generalization bounds. As a special case, we delineate a class of systems for which the number of trajectories needed to achieve epsilon-suboptimality is sublinear in the task horizon T, and do so without requiring (strong) convexity of the loss function in the policy parameters. Finally, we conduct numerical experiments demonstrating the validity of our insights on both a simple nonlinear system with tunable stability properties, and on a high-dimensional quadrupedal robotic simulation.