Fully Unconstrained Online Learning
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929366927147008 |
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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 |