Fully Unconstrained Online Learning

Fuente: arXiv
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Main Authors: Cutkosky, Ashok, Mhammedi, Zakaria
Format: Preprint
Published: 2024
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author Cutkosky, Ashok
Mhammedi, Zakaria
author_facet Cutkosky, Ashok
Mhammedi, Zakaria
contents We provide an online learning algorithm that obtains regret $G\|w_\star\|\sqrt{T\log(\|w_\star\|G\sqrt{T})} + \|w_\star\|^2 + G^2$ on $G$-Lipschitz convex losses for any comparison point $w_\star$ without knowing either $G$ or $\|w_\star\|$. Importantly, this matches the optimal bound $G\|w_\star\|\sqrt{T}$ available with such knowledge (up to logarithmic factors), unless either $\|w_\star\|$ or $G$ is so large that even $G\|w_\star\|\sqrt{T}$ is roughly linear in $T$. Thus, it matches the optimal bound in all cases in which one can achieve sublinear regret, which arguably most "interesting" scenarios.
format Preprint
id arxiv_https___arxiv_org_abs_2405_20540
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Fully Unconstrained Online Learning
Cutkosky, Ashok
Mhammedi, Zakaria
Machine Learning
Optimization and Control
We provide an online learning algorithm that obtains regret $G\|w_\star\|\sqrt{T\log(\|w_\star\|G\sqrt{T})} + \|w_\star\|^2 + G^2$ on $G$-Lipschitz convex losses for any comparison point $w_\star$ without knowing either $G$ or $\|w_\star\|$. Importantly, this matches the optimal bound $G\|w_\star\|\sqrt{T}$ available with such knowledge (up to logarithmic factors), unless either $\|w_\star\|$ or $G$ is so large that even $G\|w_\star\|\sqrt{T}$ is roughly linear in $T$. Thus, it matches the optimal bound in all cases in which one can achieve sublinear regret, which arguably most "interesting" scenarios.
title Fully Unconstrained Online Learning
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2405.20540