Regret Analysis for Randomized Gaussian Process Upper Confidence Bound

• URL: http://arxiv.org/abs/2409.00979v2
• Date: Mon, 16 Sep 2024 06:46:32 GMT
• Title: Regret Analysis for Randomized Gaussian Process Upper Confidence Bound
• Authors: Shion Takeno, Yu Inatsu, Masayuki Karasuyama,
• Abstract summary: This paper analyzes the randomized variant of GP-UCB called improved randomized GP-UCB. In both regret analyses, IRGP-UCB achieves a sub-linear regret upper bound without increasing the confidence parameter if the input domain is finite.
• Score: 9.967062483758632
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Gaussian process upper confidence bound (GP-UCB) is a theoretically established algorithm for Bayesian optimization (BO), where we assume the objective function $f$ follows GP. One notable drawback of GP-UCB is that the theoretical confidence parameter $\beta$ increased along with the iterations is too large. To alleviate this drawback, this paper analyzes the randomized variant of GP-UCB called improved randomized GP-UCB (IRGP-UCB), which uses the confidence parameter generated from the shifted exponential distribution. We analyze the expected regret and conditional expected regret, where the expectation and the probability are taken respectively with $f$ and noises and with the randomness of the BO algorithm. In both regret analyses, IRGP-UCB achieves a sub-linear regret upper bound without increasing the confidence parameter if the input domain is finite. Finally, we show numerical experiments using synthetic and benchmark functions and real-world emulators.

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