Sublinear regret for learning POMDPs

• Published in: Production and operations management 2022-09, Vol.31 (9), p.3491-3504
• Main Authors: Xiong, Yi, Chen, Ningyuan, Gao, Xuefeng, Zhou, Xiang
• Format: Article
• Language: English
• Subjects: exploration–exploitation; online learning; partially observable MDP; spectral estimator
• ISSN: 1059-1478; 1937-5956
• DOI: 10.1111/poms.13778

We study the model‐based undiscounted reinforcement learning for partially observable Markov decision processes (POMDPs). The oracle we consider is the optimal policy of the POMDP with a known environment in terms of the average reward over an infinite horizon. We propose a learning algorithm for this problem, building on spectral method‐of‐moments estimations for hidden Markov models, the belief error control in POMDPs and upper confidence bound methods for online learning. We establish a regret bound of O ( T 2 / 3 log T ) $O(T^{2/3}\sqrt {\log T})$ for the proposed learning algorithm where T is the learning horizon. This is, to the best of our knowledge, the first algorithm achieving sublinear regret with respect to our oracle for learning general POMDPs.