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arXiv · 2102.09161

On the Sample Complexity of Stability Constrained Imitation Learning

Stephen Tu·Alexander Robey·Tingnan Zhang·Nikolai Matni
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Abstract

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.

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Stephen Tu, Alexander Robey, Tingnan Zhang, Nikolai Matni. 2021-02-18. On the Sample Complexity of Stability Constrained Imitation Learning. https://arxiv.org/abs/2102.09161

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