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: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.
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: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.
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: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...
The paper introduces Gradient-based Sample Selection Bayesian Optimization (GSSBO), a method that builds the Gaussian process surrogate on a strategically chosen subset of samples rather than the full dataset. By using gradient information to eliminate redundant points while keeping diversity and representativeness, GSSBO achieves sublinear regret bounds and reduces the cubic computational cost of standard BO. Experiments on synthetic and real-world tasks show that this approach maintains comparable optimization performance while significantly cutting GP fitting time and resource usage.
arXiv:2608. 25551v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is typically analyzed at a deterministic horizon chosen before the algorithm is run, even though practical stopping decisions are made adaptively by inspecting the evolving trajectory.
arXiv:2606. 00956v1 Announce Type: new Abstract: This paper studies a one-step lookahead Bayesian optimization (BO) method and its theoretical guarantee.
arXiv:2512. 00517v3 Announce Type: replace-cross Abstract: Sequential optimization of black-box functions from noisy evaluations has been widely studied, with Gaussian Process bandit algorithms such as GP-UCB guaranteeing no-regret in stationary settings.
arXiv:2502. 01226v4 Announce Type: replace Abstract: Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions.
arXiv:2608. 03045v1 Announce Type: new Abstract: We consider grey-box optimization problems where the decision variables naturally partition into black-box variables (as arguments to an expensive black-box function) and white-box variables, governed by a set of explicit, closed-form equations that also depend on the output of the black-box function.