Improved Regret Bounds for Linear Adversarial MDPs via Linear Optimization

Published: 11 Jan 2024, Last Modified: 11 Jan 2024Accepted by TMLREveryoneRevisionsBibTeX
Abstract: Learning Markov decision processes (MDP) in an adversarial environment has been a challenging problem. The problem becomes even more challenging with function approximation since the underlying structure of the loss function and transition kernel are especially hard to estimate in a varying environment. In fact, the state-of-the-art results for linear adversarial MDP achieve a regret of $\tilde{\mathcal{O}}({K^{6/7}})$ ($K$ denotes the number of episodes), which admits a large room for improvement. In this paper, we propose a novel explore-exploit algorithm framework and investigate the problem with a new view, which reduces linear MDP into linear optimization by subtly setting the feature maps of the bandit arms of linear optimization. This new technique, under an exploratory assumption, yields an improved bound of $\tilde{\mathcal{O}}({K^{4/5}})$ for linear adversarial MDP without access to a transition simulator. The new view could be of independent interest for solving other MDP problems that possess a linear structure.
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Nishant_A_Mehta1
Submission Number: 1459