Efficient Rate Optimal Regret for Adversarial Contextual MDPs Using Online Function Approximation

Orin Levy, Alon Cohen, Asaf Cassel, Yishay Mansour

Keywords: Regret, Online function approximation, Contextual MDPs, adversarial RL

TL;DR: We study regret gurantees for adversarial contextual MDPs under the online funciton approximaiton framework.

Abstract:

We present the OMG-CMDP! algorithm for regret minimization in adversarial Contextual MDPs. The algorithm operates under the minimal assumptions of realizable function class and access to online least squares and log loss regression oracles. Our algorithm is efficient (assuming efficient online regression oracles), simple and robust to approximation errors.

It enjoys an $\widetilde{O}(H^2 \sqrt{ TH|S||A| ( \mathcal{R}_{TH}(\mathcal{O}) + H log(1/\delta)} )$ regret guarantee,
with $T$ being the number of episodes, $S$ the state space, $A$ the action space, $H$ the horizon.

In addition, $\mathcal{R}_{TH}( \mathcal{O} )$
is the sum of the square and log-loss regression oracles' regret, used to approximate the context-dependent rewards and dynamics, respectively. To the best of our knowledge, our algorithm is the first efficient rate optimal regret minimization algorithm for adversarial CMDPs that operates under the minimal standard assumption of online function approximation.

Already Accepted Paper At Another Venue: already accepted somewhere else

Submission Number: 19