arXiv Machine Learning
Regret-Based $(\epsilon,\delta)$-optimal Stopping Criteria for Bayesian Optimization
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arXiv Machine Learning
Oct 8
Pre-training of Bayesian Optimization Algorithm through Bayesian Optimization
arXiv:2610.10186v1 Announce Type: new Abstract: Bayesian optimization (BO) is widely used as a standard approach for expensive black-box optimization. However, BO algorithms often involve parameters...
arXiv Machine Learning
Jun 11
On Regret Bounds of Thompson Sampling for Bayesian Optimization
arXiv:2603. 09276v2 Announce Type: replace-cross Abstract: We study a widely used Bayesian optimization method, Gaussian process Thompson sampling (GP-TS), under the assumption that the objective function is a sample path from a GP.
arXiv Statistics ML
5d ago
Improved Regret Bounds for Gaussian Process Upper Confidence Bound in Bayesian Optimization
This paper tackles Bayesian optimization using Gaussian processes, focusing on minimizing regret when the objective function is drawn from a known GP. For a Matérn kernel with sufficient smoothness, the authors prove that the GP-UCB algorithm achieves a cumulative regret of “~O(√T) with high probability. They also establish an “O(√T ln²T)" regret bound for the squared exponential kernel, bridging the gap between previous upper bounds and Scarlett’s 2018 results. The analysis hinges on capturing the concentration of the input sequence generated by GP-UCB to refine the GP’s information‑gain estimates.
arXiv Machine Learning
Aug 4
Robust Bayesian Optimization via Tempered Posteriors
arXiv:2601. 07094v2 Announce Type: replace-cross Abstract: Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function.
arXiv Machine Learning
Oct 8
Towards Regret Guarantees for One-Step Lookahead Bayesian Optimization
The paper investigates theoretical guarantees for a one‑step lookahead Bayesian optimization method called optimal‑point variance reduction (OVR). It derives a uniform Monte Carlo estimation error bound for the acquisition function and shows that a regularized version of OVR achieves a vanishing Bayesian expected simple regret bound. Numerical experiments validate the performance of both OVR and its regularized variant.
arXiv Machine Learning
Oct 8
BONSAI: Bayesian Optimization with Natural Simplicity and Interpretability
arXiv:2602.07144v3 Announce Type: replace Abstract: Bayesian optimization (BO) is a popular technique for sample-efficient optimization of black-box functions. In many applications, the parameters be...