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Distributionally Robust Off-Dynamics Reinforcement Learning: Provable Efficiency with Linear Function Approximation

Publication ,  Conference
Liu, Z; Xu, P
Published in: Proceedings of Machine Learning Research
January 1, 2024

We study off-dynamics Reinforcement Learning (RL), where the policy is trained on a source domain and deployed to a distinct target domain. We aim to solve this problem via online distributionally robust Markov decision processes (DRMDPs), where the learning algorithm actively interacts with the source domain while seeking the optimal performance under the worst possible dynamics that is within an uncertainty set of the source domain’s transition kernel. We provide the first study on online DRMDPs with function approximation for off-dynamics RL. We find that DRMDPs’ dual formulation can induce nonlinearity, even when the nominal transition kernel is linear, leading to error propagation. By designing a d-rectangular uncertainty set using the total variation distance, we remove this additional nonlinearity and bypass the error propagation. We then introduce DR-LSVI-UCB, the first provably efficient online DRMDP algorithm for off-dynamics RL with function approximation, and establish a polynomial suboptimality bound that is independent of the state and action space sizes. Our work makes the first step towards a deeper understanding of the provable efficiency of online DRMDPs with linear function approximation. Finally, we substantiate the performance and robustness of DR-LSVI-UCB through different numerical experiments.

Duke Scholars

Published In

Proceedings of Machine Learning Research

EISSN

2640-3498

Publication Date

January 1, 2024

Volume

238

Start / End Page

2719 / 2727
 

Citation

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MLA
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Liu, Z., & Xu, P. (2024). Distributionally Robust Off-Dynamics Reinforcement Learning: Provable Efficiency with Linear Function Approximation. In Proceedings of Machine Learning Research (Vol. 238, pp. 2719–2727).

Published In

Proceedings of Machine Learning Research

EISSN

2640-3498

Publication Date

January 1, 2024

Volume

238

Start / End Page

2719 / 2727