2023/10/23 by Wonyoung Kim, Kim, Wonyoung, Garud Iyengar +3 · 1 citation
Computer Science · Engineering · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Reinforcement Learning in Robotics #Smart Grid Energy Management
paper · pdf · doi:10.48550/arxiv.2310.15286
openalex publication_date 2023/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new regret minimization algorithm for episodic sparse linear Markov decision process (SMDP) where the state-transition distribution is a linear function of observed features. The only previously known algorithm for SMDP requires the knowledge of the sparsity parameter and oracle access to an unknown policy. We overcome these limitations by combining the doubly robust method that allows one to use feature vectors of all actions with a novel analysis technique that enables the algorithm to use data from all periods in all episodes. The regret of the proposed algorithm is O(σ-1min s⋆ H √(N)), where σmin denotes the restrictive the minimum eigenvalue of the average Gram matrix of feature vectors, s_⋆ is the sparsity parameter, H is the length of an episode, and N is the number of rounds. We provide a lower regret bound that matches the upper bound up to logarithmic factors on a newly identified subclass of SMDPs. Our numerical experiments support our theoretical results and demonstrate the superior performance of our algorithm.