Skip to content

Commit

Permalink
fix bubeck19*, busa-fekete19a
Browse files Browse the repository at this point in the history
  • Loading branch information
djhsu committed Jun 19, 2019
1 parent 8cc9135 commit a6f4f71
Show file tree
Hide file tree
Showing 6 changed files with 72 additions and 31 deletions.
42 changes: 15 additions & 27 deletions _posts/2019-06-25-bubeck19a.md
Original file line number Diff line number Diff line change
@@ -1,41 +1,29 @@
---
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.
abstract: We propose a near-optimal method for highly smooth convex optimization. More precisely, in the oracle model where one obtains the $p^{th}$ order Taylor expansion of a function at the query point, we propose a method with rate of convergence $\tilde{O}(1/k^{\frac{ 3p +1}{2}})$ after $k$ queries to the oracle for any convex function whose $p^{th}$ order derivative is Lipschitz.
section: contributed
title: Improved Path-length Regret Bounds for Bandits
title: Near-optimal method for highly smooth convex optimization
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
tex_title: Near-optimal method for highly smooth convex optimization
firstpage: 492
lastpage: 507
page: 492-507
order: 492
cycles: false
bibtex_author: Bubeck, S{\'e}bastien and Li, Yuanzhi and Luo, Haipeng and Wei, Chen-Yu
bibtex_author: Bubeck, S{\'e}bastien and Jiang, Qijia and Lee, Yin Tat and Li, Yuanzhi and Sidford, Aaron
author:
- given: Sébastien
family: Bubeck
- given: Qijia
family: Jiang
- given: Yin Tat
family: Lee
- given: Yuanzhi
family: Li
- given: Haipeng
family: Luo
- given: Chen-Yu
family: Wei
- given: Aaron
family: Sidford
date: 2019-06-25
address:
publisher: PMLR
Expand All @@ -47,7 +35,7 @@ issued:
- 2019
- 6
- 25
pdf: http://proceedings.mlr.press/v99/bubeck19a/bubeck19a.pdf
pdf: http://proceedings.mlr.press/v99/bubeck19b/bubeck19a.pdf
extras: []
# Format based on citeproc: http://blog.martinfenner.org/2013/07/30/citeproc-yaml-for-bibliographies/
---
53 changes: 53 additions & 0 deletions _posts/2019-06-25-bubeck19b.md
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/
---
Original file line number Diff line number Diff line change
Expand Up @@ -20,19 +20,19 @@ section: contributed
title: Optimal Learning of Mallows Block Model
layout: inproceedings
series: Proceedings of Machine Learning Research
id: buda-fekete19a
id: busa-fekete19a
month: 0
tex_title: Optimal Learning of Mallows Block Model
firstpage: 529
lastpage: 532
page: 529-532
order: 529
cycles: false
bibtex_author: Buda-Fekete, Robert and Fotakis, Dimitris and Sz\"{o}r\'enyi, Bal\'{a}zs
bibtex_author: Busa-Fekete, Robert and Fotakis, Dimitris and Sz\"{o}r\'enyi, Bal\'{a}zs
and Zampetakis, Manolis
author:
- given: Robert
family: Buda-Fekete
family: Busa-Fekete
- given: Dimitris
family: Fotakis
- given: Balázs
Expand All @@ -50,7 +50,7 @@ issued:
- 2019
- 6
- 25
pdf: http://proceedings.mlr.press/v99/buda-fekete19a/buda-fekete19a.pdf
pdf: http://proceedings.mlr.press/v99/busa-fekete19a/busa-fekete19a.pdf
extras: []
# Format based on citeproc: http://blog.martinfenner.org/2013/07/30/citeproc-yaml-for-bibliographies/
---
Binary file modified bubeck19a/bubeck19a.pdf
Binary file not shown.
Binary file added bubeck19b/bubeck19b.pdf
Binary file not shown.
File renamed without changes.

0 comments on commit a6f4f71

Please sign in to comment.