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arXiv · 2212.00186

Multi-Task Imitation Learning for Linear Dynamical Systems

Thomas T. Zhang·Katie Kang·Bruce D. Lee·Claire Tomlin·Sergey Levine·Stephen Tu·Nikolai Matni
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Abstract

We study representation learning for efficient imitation learning over linear systems. In particular, we consider a setting where learning is split into two phases: (a) a pre-training step where a shared $k$-dimensional representation is learned from $H$ source policies, and (b) a target policy fine-tuning step where the learned representation is used to parameterize the policy class. We find that the imitation gap over trajectories generated by the learned target policy is bounded by $\tilde{O}\left( \frac{k n_x}{HN_{\mathrm{shared}}} + \frac{k n_u}{N_{\mathrm{target}}}\right)$, where $n_x > k$ is the state dimension, $n_u$ is the input dimension, $N_{\mathrm{shared}}$ denotes the total amount of data collected for each policy during representation learning, and $N_{\mathrm{target}}$ is the amount of target task data. This result formalizes the intuition that aggregating data across related tasks to learn a representation can significantly improve the sample efficiency of learning a target task. The trends suggested by this bound are corroborated in simulation.

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BibTeXRIS

Thomas T. Zhang, Katie Kang, Bruce D. Lee, Claire Tomlin, Sergey Levine, Stephen Tu, Nikolai Matni. 2023-11-10. Multi-Task Imitation Learning for Linear Dynamical Systems. https://arxiv.org/abs/2212.00186

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