Reinforcement Learning in Linear MDPs: Constant Regret and Representation Selection
Matteo Papini, Andrea Tirinzoni, Aldo Pacchiano, Marcello Restelli, Alessandro Lazaric, Matteo Pirotta
Abstract
We study the role of the representation of state-action value functions in regret minimization in finite-horizon Markov Decision Processes (MDPs) with linear structure. We first derive a necessary condition on the representation, called universally spanning optimal features (UNISOFT), to achieve constant regret in any MDP with linear reward function. This result encompasses the well-known settings of low-rank MDPs and, more generally, zero inherent Bellman error (also known as the Bellman closure assumption). We then demonstrate that this condition is also sufficient for these classes of problems by deriving a constant regret bound for two optimistic algorithms (LSVI-UCB and ELEANOR). Finally, we propose an algorithm for representation selection and we prove that it achieves constant regret when one of the given representations, or a suitable combination of them, satisfies the UNISOFT condition.
BibTeX
@inproceedings{
papini2021reinforcement,
title={Reinforcement Learning in Linear {MDP}s: Constant Regret and Representation Selection},
author={Matteo Papini and Andrea Tirinzoni and Aldo Pacchiano and Marcello Restelli and Alessandro Lazaric and Matteo Pirotta},
booktitle={Advances in Neural Information Processing Systems},
editor={A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
year={2021},
url={https://openreview.net/forum?id=t0r2M-ndcaJ}
}