Density-Based Algorithms for Corruption-Robust Contextual Search and Convex Optimization
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866912798350508032 |
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| author | Leme, Renato Paes Podimata, Chara Schneider, Jon |
| author_facet | Leme, Renato Paes Podimata, Chara Schneider, Jon |
| contents | We study the problem of contextual search, a generalization of binary search in higher dimensions, in the adversarial noise model. Let $d$ be the dimension of the problem, $T$ be the time horizon and $C$ be the total amount of adversarial noise in the system. We focus on the $ε$-ball and the symmetric loss. For the $ε$-ball loss, we give a tight regret bound of $O(C + d \log(1/ε))$ improving over the $O(d^3 \log(1/ε) \log^2(T) + C \log(T) \log(1/ε))$ bound of Krishnamurthy et al (Operations Research '23). For the symmetric loss, we give an efficient algorithm with regret $O(C+d \log T)$. To tackle the symmetric loss case, we study the more general setting of Corruption-Robust Convex Optimization with Subgradient feedback, which is of independent interest.
Our techniques are a significant departure from prior approaches. Specifically, we keep track of density functions over the candidate target vectors instead of a knowledge set consisting of the candidate target vectors consistent with the feedback obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_07528 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Density-Based Algorithms for Corruption-Robust Contextual Search and Convex Optimization Leme, Renato Paes Podimata, Chara Schneider, Jon Machine Learning Computer Science and Game Theory We study the problem of contextual search, a generalization of binary search in higher dimensions, in the adversarial noise model. Let $d$ be the dimension of the problem, $T$ be the time horizon and $C$ be the total amount of adversarial noise in the system. We focus on the $ε$-ball and the symmetric loss. For the $ε$-ball loss, we give a tight regret bound of $O(C + d \log(1/ε))$ improving over the $O(d^3 \log(1/ε) \log^2(T) + C \log(T) \log(1/ε))$ bound of Krishnamurthy et al (Operations Research '23). For the symmetric loss, we give an efficient algorithm with regret $O(C+d \log T)$. To tackle the symmetric loss case, we study the more general setting of Corruption-Robust Convex Optimization with Subgradient feedback, which is of independent interest. Our techniques are a significant departure from prior approaches. Specifically, we keep track of density functions over the candidate target vectors instead of a knowledge set consisting of the candidate target vectors consistent with the feedback obtained. |
| title | Density-Based Algorithms for Corruption-Robust Contextual Search and Convex Optimization |
| topic | Machine Learning Computer Science and Game Theory |
| url | https://arxiv.org/abs/2206.07528 |