Spectral Entry-wise Matrix Estimation for Low-Rank Reinforcement Learning

Published: 21 Sept 2023, Last Modified: 02 Nov 2023NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: Low-rank matrix estimation; low rank bandits; low rank MDP; spectral methods
TL;DR: We investigate simple spectral methods towards the entry-wise estimation of low-rank matrices arising in reinforcement learning.
Abstract: We study matrix estimation problems arising in reinforcement learning with low-rank structure. In low-rank bandits, the matrix to be recovered specifies the expected arm rewards, and for low-rank Markov Decision Processes (MDPs), it characterizes the transition kernel of the MDP. In both cases, each entry of the matrix carries important information, and we seek estimation methods with low entry-wise prediction error. Importantly, these methods further need to accommodate for inherent correlations in the available data (e.g. for MDPs, the data consists of system trajectories). We investigate the performance of simple spectral-based matrix estimation approaches: we show that they efficiently recover the singular subspaces of the matrix and exhibit nearly-minimal entry-wise prediction error. These new results on low-rank matrix estimation make it possible to devise reinforcement learning algorithms that fully exploit the underlying low-rank structure. We provide two examples of such algorithms: a regret minimization algorithm for low-rank bandit problems, and a best policy identification algorithm for low-rank MDPs. Both algorithms yield state-of-the-art performance guarantees.
Supplementary Material: pdf
Submission Number: 12586