Lenient Regret and Good-Action Identification in Gaussian Process Bandits

• URL: http://arxiv.org/abs/2102.05793v1
• Date: Thu, 11 Feb 2021 01:16:58 GMT
• Title: Lenient Regret and Good-Action Identification in Gaussian Process Bandits
• Authors: Xu Cai, Selwyn Gomes, Jonathan Scarlett
• Abstract summary: We study the problem of Gaussian process (GP) bandits under relaxed optimization criteria stating that any function value above a certain threshold is "good enough" On the practical side, we consider the problem of finding a single "good action" according to a known pre-specified threshold, and introduce several good-action identification algorithms that exploit knowledge of the threshold.
• Score: 43.03669155559218
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study the problem of Gaussian process (GP) bandits under relaxed optimization criteria stating that any function value above a certain threshold is "good enough". On the theoretical side, we study various \emph{\lenient regret} notions in which all near-optimal actions incur zero penalty, and provide upper bounds on the lenient regret for GP-UCB and an elimination algorithm, circumventing the usual $O(\sqrt{T})$ term (with time horizon $T$) resulting from zooming extremely close towards the function maximum. In addition, we complement these upper bounds with algorithm-independent lower bounds. On the practical side, we consider the problem of finding a single "good action" according to a known pre-specified threshold, and introduce several good-action identification algorithms that exploit knowledge of the threshold. We experimentally find that such algorithms can often find a good action faster than standard optimization-based approaches.

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