Learning Infinite-Horizon Average-Reward Markov Decision Processes with Constraints

• URL: http://arxiv.org/abs/2202.00150v1
• Date: Mon, 31 Jan 2022 23:52:34 GMT
• Title: Learning Infinite-Horizon Average-Reward Markov Decision Processes with Constraints
• Authors: Liyu Chen, Rahul Jain, Haipeng Luo
• Abstract summary: We study regret for infinite-horizon average-reward Markov Decision Processes (MDPs) under cost constraints. Our algorithm ensures $widetildeO(sqrtT)$ regret and constant constraint violation for ergodic MDPs. These are the first set of provable algorithms for weakly communicating MDPs with cost constraints.
• Score: 39.715977181666766
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study regret minimization for infinite-horizon average-reward Markov Decision Processes (MDPs) under cost constraints. We start by designing a policy optimization algorithm with carefully designed action-value estimator and bonus term, and show that for ergodic MDPs, our algorithm ensures $\widetilde{O}(\sqrt{T})$ regret and constant constraint violation, where $T$ is the total number of time steps. This strictly improves over the algorithm of (Singh et al., 2020), whose regret and constraint violation are both $\widetilde{O}(T^{2/3})$. Next, we consider the most general class of weakly communicating MDPs. Through a finite-horizon approximation, we develop another algorithm with $\widetilde{O}(T^{2/3})$ regret and constraint violation, which can be further improved to $\widetilde{O}(\sqrt{T})$ via a simple modification, albeit making the algorithm computationally inefficient. As far as we know, these are the first set of provable algorithms for weakly communicating MDPs with cost constraints.

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