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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | https://arxiv.org/abs/2307.13903 |
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| _version_ | 1866913218107015168 |
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| author | Zuo, Shiliang |
| author_facet | Zuo, Shiliang |
| contents | I study the problem of learning a Lipschitz function with corrupted binary signals. The learner tries to learn a $L$-Lipschitz function $f: [0,1]^d \rightarrow [0, L]$ that the adversary chooses. There is a total of $T$ rounds. In each round $t$, the adversary selects a context vector $x_t$ in the input space, and the learner makes a guess to the true function value $f(x_t)$ and receives a binary signal indicating whether the guess is high or low. In a total of $C$ rounds, the signal may be corrupted, though the value of $C$ is \emph{unknown} to the learner. The learner's goal is to incur a small cumulative loss. This work introduces the new algorithmic technique \emph{agnostic checking} as well as new analysis techniques. I design algorithms which: for the symmetric loss, the learner achieves regret $L\cdot O(C\log T)$ with $d = 1$ and $L\cdot O_d(C\log T + T^{(d-1)/d})$ with $d > 1$; for the pricing loss, the learner achieves regret $L\cdot \widetilde{O} (T^{d/(d+1)} + C\cdot T^{1/(d+1)})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13903 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Corruption-Robust Lipschitz Contextual Search Zuo, Shiliang Machine Learning I study the problem of learning a Lipschitz function with corrupted binary signals. The learner tries to learn a $L$-Lipschitz function $f: [0,1]^d \rightarrow [0, L]$ that the adversary chooses. There is a total of $T$ rounds. In each round $t$, the adversary selects a context vector $x_t$ in the input space, and the learner makes a guess to the true function value $f(x_t)$ and receives a binary signal indicating whether the guess is high or low. In a total of $C$ rounds, the signal may be corrupted, though the value of $C$ is \emph{unknown} to the learner. The learner's goal is to incur a small cumulative loss. This work introduces the new algorithmic technique \emph{agnostic checking} as well as new analysis techniques. I design algorithms which: for the symmetric loss, the learner achieves regret $L\cdot O(C\log T)$ with $d = 1$ and $L\cdot O_d(C\log T + T^{(d-1)/d})$ with $d > 1$; for the pricing loss, the learner achieves regret $L\cdot \widetilde{O} (T^{d/(d+1)} + C\cdot T^{1/(d+1)})$. |
| title | Corruption-Robust Lipschitz Contextual Search |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2307.13903 |