New Regret Bounds for Gaussian Process Upper Confidence Bound in Bayesian Optimization

This paper presents improved regret bounds for the Gaussian Process Upper Confidence Bound (GP-UCB) algorithm in Bayesian optimization. The research focuses on scenarios with a Matérn kernel, achieving a cumulative regret of \(\tilde{O}(\sqrt{T})\) with high probability, and under a squared exponential kernel, it yields $O(\sqrt{T \ln^2 T})$ regret. These findings aim to bridge a gap in the existing theoretical understanding of GP-UCB's performance. AI

IMPACT This research refines theoretical bounds for Bayesian optimization algorithms, potentially leading to more efficient exploration in machine learning tasks.

RANK_REASON The item is an academic paper detailing theoretical improvements to an algorithm. [lever_c_demoted from research: ic=1 ai=1.0]

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• arXiv
• Bayesian optimization
• Gaussian process
• Gaussian Process Upper Confidence Bound
• GP-UCB
• Matérn kernel
• Shogo Iwazaki
• Xbox Series X

• paper
• other

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