On the Sample Complexity of Stability Constrained Imitation Learning

By Stephen Tu, Alexander Robey, Tingnan Zhang, Nikolai Matni. 2021

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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 surprisingly granular connection can be made between the underlying 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. In particular, we propose and analyze incremental gain stability constrained versions of behavior cloning and a DAgger-like algorithm, and show that the resulting sample-complexity bounds naturally reflect the underlying stability properties of the expert system. As a special case, we delineate a class of systems for which the number of trajectories needed to achieve $\varepsilon$-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 for which the underlying stability properties can be easily tuned, and on a high-dimensional quadrupedal robotic simulation.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistical and Nonlinear Physics

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Citations in the corpus

Implicit Behavioral Cloning (2021, background): “, compounding 20 errors [2, 3]), in practice it enables some of the most compelling results of real robots generalizing complex 21 behaviors to new unstructured scenarios [4, 5, 6].”