2021-07-21-cohen21a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Online Markov Decision Processes with Aggregate Bandit Feedback	We study a novel variant of online finite-horizon Markov Decision Processes with adversarially changing loss functions and initially unknown dynamics. In each episode, the learner suffers the loss accumulated along the trajectory realized by the policy chosen for the episode, and observes aggregate bandit feedback: the trajectory is revealed along with the cumulative loss suffered, rather than the individual losses encountered along the trajectory. Our main result is a computationally efficient algorithm with $O(\sqrt{K})$ regret for this setting, where K is the number of episodes. We establish this result via an efficient reduction to a novel bandit learning setting we call Distorted Linear Bandits (DLB), which is a variant of bandit linear optimization where actions chosen by the learner are adversarially distorted before they are committed. We then develop a computationally-efficient online algorithm for DLB for which we prove an $O(\sqrt{T})$ regret bound, where T is the number of time steps. Our algorithm is based on online mirror descent with a self-concordant barrier regularization that employs a novel increasing learning rate schedule.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	cohen21a	0	Online Markov Decision Processes with Aggregate Bandit Feedback	1301	1329	1301-1329	1301	false	Cohen, Alon and Kaplan, Haim and Koren, Tomer and Mansour, Yishay	given family Alon Cohen given family Haim Kaplan given family Tomer Koren given family Yishay Mansour	2021-07-21		Proceedings of Thirty Fourth Conference on Learning Theory	134	inproceedings	date-parts 2021 7 21	http://proceedings.mlr.press/v134/cohen21a/cohen21a.pdf