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Upper Confidence Primal-Dual Reinforcement Learning for CMDP with Adversarial Loss
Shuang Qiu · Xiaohan Wei · Zhuoran Yang · Jieping Ye · Zhaoran Wang

Mon Dec 07 09:00 PM -- 11:00 PM (PST) @ Poster Session 0 #171
We consider online learning for episodic stochastically constrained Markov decision processes (CMDP), which plays a central role in ensuring the safety of reinforcement learning. Here the loss function can vary arbitrarily across the episodes, and both the loss received and the budget consumption are revealed at the end of each episode. Previous works solve this problem under the restrictive assumption that the transition model of the MDP is known a priori and establish regret bounds that depend polynomially on the cardinalities of the state space $\mathcal{S}$ and the action space $\mathcal{A}$. In this work, we propose a new \emph{upper confidence primal-dual} algorithm, which only requires the trajectories sampled from the transition model. In particular, we prove that the proposed algorithm achieves $\widetilde{\mathcal{O}}(L|\mathcal{S}|\sqrt{|\mathcal{A}|T})$ upper bounds of both the regret and the constraint violation, where $L$ is the length of each episode. Our analysis incorporates a new high-probability drift analysis of Lagrange multiplier processes into the celebrated regret analysis of upper confidence reinforcement learning, which demonstrates the power of ``optimism in the face of uncertainty'' in constrained online learning.

Author Information

Shuang Qiu (University of Michigan)
Xiaohan Wei (University of Southern California)
Zhuoran Yang (Princeton)
Jieping Ye (University of Michigan)
Zhaoran Wang (Northwestern University)

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