Multi-Task Imitation Learning for Linear Dynamical Systems

Thomas T. Zhang, Katie Kang, Bruce D Lee, Claire Tomlin, Sergey Levine, Stephen Tu, Nikolai Matni
Proceedings of The 5th Annual Learning for Dynamics and Control Conference, PMLR 211:586-599, 2023.

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 ˜O(knxHNshared+knuNtarget), where nx>k is the state dimension, nu is the input dimension, Nshared denotes the total amount of data collected for each policy during representation learning, and Ntarget 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v211-zhang23b, title = {Multi-Task Imitation Learning for Linear Dynamical Systems}, author = {Zhang, Thomas T. and Kang, Katie and Lee, Bruce D and Tomlin, Claire and Levine, Sergey and Tu, Stephen and Matni, Nikolai}, booktitle = {Proceedings of The 5th Annual Learning for Dynamics and Control Conference}, pages = {586--599}, year = {2023}, editor = {Matni, Nikolai and Morari, Manfred and Pappas, George J.}, volume = {211}, series = {Proceedings of Machine Learning Research}, month = {15--16 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v211/zhang23b/zhang23b.pdf}, url = {https://proceedings.mlr.press/v211/zhang23b.html}, 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. } }
Endnote
%0 Conference Paper %T Multi-Task Imitation Learning for Linear Dynamical Systems %A Thomas T. Zhang %A Katie Kang %A Bruce D Lee %A Claire Tomlin %A Sergey Levine %A Stephen Tu %A Nikolai Matni %B Proceedings of The 5th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2023 %E Nikolai Matni %E Manfred Morari %E George J. Pappas %F pmlr-v211-zhang23b %I PMLR %P 586--599 %U https://proceedings.mlr.press/v211/zhang23b.html %V 211 %X 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.
APA
Zhang, T.T., Kang, K., Lee, B.D., Tomlin, C., Levine, S., Tu, S. & Matni, N.. (2023). Multi-Task Imitation Learning for Linear Dynamical Systems. Proceedings of The 5th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 211:586-599 Available from https://proceedings.mlr.press/v211/zhang23b.html.

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