Regret Analysis for Randomized Gaussian Process Upper Confidence Bound
| Autor: | Takeno, Shion, Inatsu, Yu, Karasuyama, Masayuki |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 31 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2302.01511 |
| Databáze: | arXiv |
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