2019-06-25-bubeck19b.md

abstract	section	title	layout	series	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	publisher	container-title	volume	genre	issued	pdf	extras
We study adaptive regret bounds in terms of the variation of the losses (the so-called path-length bounds) for both multi-armed bandit and more generally linear bandit. We first show that the seemingly suboptimal path-length bound of (Wei and Luo, 2018) is in fact not improvable for adaptive adversary. Despite this negative result, we then develop two new algorithms, one that strictly improves over (Wei and Luo, 2018) with a smaller path-length measure, and the other which improves over (Wei and Luo, 2018) for oblivious adversary when the path-length is large. Our algorithms are based on the well-studied optimistic mirror descent framework, but importantly with several novel techniques, including new optimistic predictions, a slight bias towards recently selected arms, and the use of a hybrid regularizer similar to that of (Bubeck et al., 2018). Furthermore, we extend our results to linear bandit by showing a reduction to obtaining dynamic regret for a full-information problem, followed by a further reduction to convex body chasing. As a consequence we obtain new dynamic regret results as well as the first path-length regret bounds for general linear bandit.	contributed	Improved Path-length Regret Bounds for Bandits	inproceedings	Proceedings of Machine Learning Research	bubeck19b	0	Improved Path-length Regret Bounds for Bandits	508	528	508-528	508	false	Bubeck, S{\'e}bastien and Li, Yuanzhi and Luo, Haipeng and Wei, Chen-Yu	given family Sébastien Bubeck given family Yuanzhi Li given family Haipeng Luo given family Chen-Yu Wei	2019-06-25		PMLR	Proceedings of the Thirty-Second Conference on Learning Theory	99	inproceedings	date-parts 2019 6 25	http://proceedings.mlr.press/v99/bubeck19b/bubeck19b.pdf