No-Regret Algorithms for Time-Varying Bayesian Optimization

• URL: http://arxiv.org/abs/2102.06296v1
• Date: Thu, 11 Feb 2021 22:35:32 GMT
• Title: No-Regret Algorithms for Time-Varying Bayesian Optimization
• Authors: Xingyu Zhou and Ness Shroff
• Abstract summary: We adopt the general variation budget model to capture the time-varying environment. We introduce two GP-UCB type algorithms: R-GP-UCB and SW-GP-UCB, respectively. Our results not only recover previous linear bandit results when a linear kernel is used, but complement the previous regret analysis of time-varying Gaussian process bandit.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we consider the time-varying Bayesian optimization problem. The unknown function at each time is assumed to lie in an RKHS (reproducing kernel Hilbert space) with a bounded norm. We adopt the general variation budget model to capture the time-varying environment, and the variation is characterized by the change of the RKHS norm. We adapt the restart and sliding window mechanism to introduce two GP-UCB type algorithms: R-GP-UCB and SW-GP-UCB, respectively. We derive the first (frequentist) regret guarantee on the dynamic regret for both algorithms. Our results not only recover previous linear bandit results when a linear kernel is used, but complement the previous regret analysis of time-varying Gaussian process bandit under a Bayesian-type regularity assumption, i.e., each function is a sample from a Gaussian process.

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