-
Notifications
You must be signed in to change notification settings - Fork 2
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Showing
6 changed files
with
72 additions
and
31 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,53 @@ | ||
--- | ||
abstract: 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. | ||
section: contributed | ||
title: Improved Path-length Regret Bounds for Bandits | ||
layout: inproceedings | ||
series: Proceedings of Machine Learning Research | ||
id: bubeck19a | ||
month: 0 | ||
tex_title: Improved Path-length Regret Bounds for Bandits | ||
firstpage: 508 | ||
lastpage: 528 | ||
page: 508-528 | ||
order: 508 | ||
cycles: false | ||
bibtex_author: Bubeck, S{\'e}bastien and Li, Yuanzhi and Luo, Haipeng and Wei, Chen-Yu | ||
author: | ||
- given: Sébastien | ||
family: Bubeck | ||
- given: Yuanzhi | ||
family: Li | ||
- given: Haipeng | ||
family: Luo | ||
- given: Chen-Yu | ||
family: Wei | ||
date: 2019-06-25 | ||
address: | ||
publisher: PMLR | ||
container-title: Proceedings of the Thirty-Second Conference on Learning Theory | ||
volume: '99' | ||
genre: inproceedings | ||
issued: | ||
date-parts: | ||
- 2019 | ||
- 6 | ||
- 25 | ||
pdf: http://proceedings.mlr.press/v99/bubeck19a/bubeck19a.pdf | ||
extras: [] | ||
# Format based on citeproc: http://blog.martinfenner.org/2013/07/30/citeproc-yaml-for-bibliographies/ | ||
--- |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Binary file not shown.
Binary file not shown.
File renamed without changes.