arXiv:2511. 16340v2 Announce Type: replace Abstract: Efficient Gaussian process (GP) inference is critical for sequential decision-making tasks such as active learning, online prediction, and 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: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:2507.06529v2 Announce Type: replace Abstract: Bayesian optimization (BO) is a powerful paradigm for optimizing expensive black-box functions. Traditional BO methods typically rely on separate h...
arXiv:2606. 02351v1 Announce Type: new Abstract: Bayesian optimization (BO) is a popular and effective approach for tuning expensive, noisy experiments, but requires the formulation of an explicit objective function.
The paper investigates how fast predictive regret guarantees of exact Bayesian online learning can be maintained when using approximate posterior methods. It establishes a general theorem linking the cumulative cost of posterior approximation to the contraction radius of the exact Gibbs posterior and the Wasserstein distance between approximate and exact posteriors. Three concrete online learning scenarios—linear models, infinite‑dimensional exponential families, and Gaussian process regression—illustrate that appropriately accurate approximations (projected Langevin, truncation, and sparse variational posteriors) preserve fast regret bounds while reducing computational demands.
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:2502. 01226v4 Announce Type: replace Abstract: Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions.
The paper analyzes Bayesian linear bandits with isotropic Gaussian parameters, independent Gaussian arms, and Gaussian reward noise when the time horizon scales with the dimension. It derives explicit limits for the normalized posterior uncertainty and parameter overlaps, yielding exact regret curves for several policies—including Thompson sampling, posterior‑mean greedy selection, and scaled‑covariance variants. The results show that posterior‑mean greedy selection achieves the optimal Bayes regret, while Thompson sampling incurs a strictly larger leading regret whose ratio to greedy lies between one and two, approaching two for long horizons.
arXiv:2605.22561v2 Announce Type: replace Abstract: Bayesian optimization (BO) is a widely used iterative black-box optimization method that utilizes Gaussian process (GP) surrogate models. In practi...
arXiv:2610.19925v1 Announce Type: cross Abstract: Efficient global optimization aims to identify a global optimum of an expensive black-box function within a limited evaluation budget $N$. We investi...
The paper tackles two shortcomings of Gaussian‑process based active learning: (1) the posterior variance is independent of observed values, reducing sensitivity to data structure, and (2) it over‑inflates variance near domain boundaries, causing excessive edge sampling. The authors propose a reconstruction‑driven design density that warps sampling toward regions where the posterior mean changes rapidly, and a geometric equalizer that corrects boundary bias. Experiments on sixteen synthetic and two real‑data benchmarks show that the equalizer consistently improves function reconstruction, while the warp further enhances performance by concentrating measurements where the target function varies most.