From a6f4f719c33d8811928babe280a581b672d699fd Mon Sep 17 00:00:00 2001 From: Daniel Hsu Date: Wed, 19 Jun 2019 08:58:38 -0700 Subject: [PATCH] fix bubeck19*, busa-fekete19a --- _posts/2019-06-25-bubeck19a.md | 42 +++++--------- _posts/2019-06-25-bubeck19b.md | 53 ++++++++++++++++++ ...ete19a.md => 2019-06-25-busa-fekete19a.md} | 8 +-- bubeck19a/bubeck19a.pdf | Bin 411645 -> 268737 bytes bubeck19b/bubeck19b.pdf | Bin 0 -> 411645 bytes .../busa-fekete19a.pdf | Bin 6 files changed, 72 insertions(+), 31 deletions(-) create mode 100644 _posts/2019-06-25-bubeck19b.md rename _posts/{2019-06-25-buda-fekete19a.md => 2019-06-25-busa-fekete19a.md} (92%) create mode 100755 bubeck19b/bubeck19b.pdf rename buda-fekete19a/buda-fekete19a.pdf => busa-fekete19a/busa-fekete19a.pdf (100%) diff --git a/_posts/2019-06-25-bubeck19a.md b/_posts/2019-06-25-bubeck19a.md index 28efdec..1806e11 100644 --- a/_posts/2019-06-25-bubeck19a.md +++ b/_posts/2019-06-25-bubeck19a.md @@ -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 @@ -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/ --- diff --git a/_posts/2019-06-25-bubeck19b.md b/_posts/2019-06-25-bubeck19b.md new file mode 100644 index 0000000..28efdec --- /dev/null +++ b/_posts/2019-06-25-bubeck19b.md @@ -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/ +--- diff --git a/_posts/2019-06-25-buda-fekete19a.md b/_posts/2019-06-25-busa-fekete19a.md similarity index 92% rename from _posts/2019-06-25-buda-fekete19a.md rename to _posts/2019-06-25-busa-fekete19a.md index 8a577cb..71e8b3f 100644 --- a/_posts/2019-06-25-buda-fekete19a.md +++ b/_posts/2019-06-25-busa-fekete19a.md @@ -20,7 +20,7 @@ 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 @@ -28,11 +28,11 @@ 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 @@ -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/ --- diff --git a/bubeck19a/bubeck19a.pdf b/bubeck19a/bubeck19a.pdf index 2a3b4dfeae845d6de2f1cdcdaf1817ef120dfcaf..6dd3b5a9c80914700a79c1bf18f02eae93d2b4c1 100755 GIT binary patch delta 253389 zcmV)BK*PWNj~T(U5D+C$L`E$!E;R}z(A34)3O1LKp8*pCGchri7y>DO-CA37+cp+{ z_pi{tbf{^C5&(%yI+Xv`p#Z>|&wQh0HRNX8Gc5v-m0bSKF-1a#Pip z-Ezh9G-)o}@6%$vt?JT$-TY7%ZH+bV?q%8Ge!X>f@0JWt?c9yl50<~2eRq;#d%9>1 z7v|#SHz(MO`YFd727YEt+_PL9um8+#!cwZ2E1D`v6VB?58$GS-tHQJKxT!D7wyf8l z|E7+e<7`_t?ageHyM7_XY(X=^Gr^1)IVCw=tVBj+CY&Unf%cMr%VgCY`f5LLvM>8> z<2k%ovOH;8ceAZ7x4Rp6-R+yE_u^cG*UU(jrb+p`XWvk)-WPp^NwDjD%j(h9dAWY;w+l^(X$?7m 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