[2603.25311] Practical Efficient Global Optimization is No-regret

Statistics > Machine Learning arXiv:2603.25311 (stat) [Submitted on 26 Mar 2026] Title:Practical Efficient Global Optimization is No-regret Authors:Jingyi Wang, Haowei Wang, Nai-Yuan Chiang, Juliane Mueller, Tucker Hartland, Cosmin G. Petra View a PDF of the paper titled Practical Efficient Global Optimization is No-regret, by Jingyi Wang and 5 other authors View PDF HTML (experimental) Abstract:Efficient global optimization (EGO) is one of the most widely used noise-free Bayesian optimization this http URL comprises the Gaussian process (GP) surrogate model and expected improvement (EI) acquisition function. In practice, when EGO is applied, a scalar matrix of a small positive value (also called a nugget or jitter) is usually added to the covariance matrix of the deterministic GP to improve numerical stability. We refer to this EGO with a positive nugget as the practical EGO. Despite its wide adoption and empirical success, to date, cumulative regret bounds for practical EGO have yet to be established. In this paper, we present for the first time the cumulative regret upper bound of practical EGO. In particular, we show that practical EGO has sublinear cumulative regret bounds and thus is a no-regret algorithm for commonly used kernels including the squared exponential (SE) and Matérn kernels ($\nu>\frac{1}{2}$). Moreover, we analyze the effect of the nugget on the regret bound and discuss the theoretical implication on its choice. Numerical experiments are conducted to s...