Corruption-Robust Lipschitz Contextual Search

• URL: http://arxiv.org/abs/2307.13903v4
• Date: Thu, 1 Feb 2024 08:11:55 GMT
• Title: Corruption-Robust Lipschitz Contextual Search
• Authors: Shiliang Zuo
• Abstract summary: I study the problem of learning a Lipschitz function with corrupted binary signals. This work introduces the new algorithmic technique emphagnostic checking as well as new analysis techniques.
• Score: 2.296475290901356
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $L\cdot \widetilde{O} (T^{d/(d+1)} + C\cdot T^{1/(d+1)})$.

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