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# A Primal-Dual Algorithm for Offline Constrained Reinforcement Learning with Linear MDPs

*Proceedings of the 41st International Conference on Machine Learning*, PMLR 235:18711-18737, 2024.

#### Abstract

We study offline reinforcement learning (RL) with linear MDPs under the infinite-horizon discounted setting which aims to learn a policy that maximizes the expected discounted cumulative reward using a pre-collected dataset. Existing algorithms for this setting either require a uniform data coverage assumptions or are computationally inefficient for finding an $\epsilon$-optimal policy with $\mathcal{O}(\epsilon^{-2})$ sample complexity. In this paper, we propose a primal dual algorithm for offline RL with linear MDPs in the infinite-horizon discounted setting. Our algorithm is the first computationally efficient algorithm in this setting that achieves sample complexity of $\mathcal{O}(\epsilon^{-2})$ with partial data coverage assumption. Our work is an improvement upon a recent work that requires $\mathcal{O}(\epsilon^{-4})$ samples. Moreover, we extend our algorithm to work in the offline constrained RL setting that enforces constraints on additional reward signals.