STREGO: A Scalable Implementation of a Trust-Region Framework for Noisy Bayesian Optimization

Youssef Diouane; Issmail El Hallaoui; Meisseme Kadri; Amina Lamghari

math.OCOct 9, 2026

STREGO: A Scalable Implementation of a Trust-Region Framework for Noisy Bayesian Optimization

Authors: Youssef Diouane, Issmail El Hallaoui, Meisseme Kadri, Amina Lamghari

Organizations: GERAD & Department of Mathematics and Industrial Engineering, Polytechnique Montr´eal. · GERAD & Department of Management, Universit´e du Qu´ebec `a Trois-Rivi`eres.

Abstract

TREGO, a trust-region Bayesian optimization (BO) method for expensive blackbox problems, has convergence guarantees, but only for exact function values. In high dimension, its performance tends to deteriorate. This paper asks whether a trust-region BO method can be extended to handle noisy evaluations while being competitive in high dimension. We first generalize TREGO into a trust-region framework for noisy BO and extend its convergence analysis to noisy function estimates that are sufficiently accurate with sufficiently high probability. We then propose STREGO, a scalable implementation of this framework. Its global phase selects a batch of candidates by solving a bi-objective problem on the posterior mean of a Gaussian process and the integrated variance reduction. Unlike the predictive variance, this second objective does not favor boundary points merely because they are far from the data. Its local phase minimizes the posterior mean of a second Gaussian process, trained only on points close to the incumbent. STREGO is compared with TREGO, TURBO, BAXUS and NSMA-BO on synthetic and real-world problems of dimension $4$ to $124$ , with and without noise. It gives the best average results in every synthetic setting tested and the best or tied-best solution on four of the six real-world problems. An implementation of STREGO is available at https://github.com/Mayousk/STREGO.

Figures & tables

Panel of Figure 1 — Figure 1: Overview of TREGO, adapted from [ 16 ] (here $0<\beta<1<\gamma$ ).

Panel of Figure 2 — Figure 2: An $\mathbb{R}^{2}$ illustration of the annular trust region $\overline{\Omega}_{k}$ (using the infinity norm) for different step sizes and incumbent positions $x_{k}\in\Omega$ .

\overline{\mathcal{X}}=\bigl\{x\in\mathcal{X}\;\big|\;\|x-x_{k}\|\leq\rho\,r_{\max}\delta_{k}\bigr\},

Algorithm 3 Step 3 of Algorithm 1 .

Figure 3: Comparison of STREGO with the global bi-objective criterion $(\mu,-\mathrm{IVR})$ against its variance counterpart $(\mu,-\sigma^{2})$ , both using the exploitative local phase, on Ackley, Alpine-01, Rotated Rastrigin and Schwefel in $4$ d, $20$ d, $50$ d and $100$ d under different noise settings.

Figure 4: Normalized final objective value (lower is better) and CPU time for $d=20$ , 50 and 100 in the noise-free setting. Tables report the mean $\pm$ standard error over 20 trials and 5 functions.

Figure 5: Normalized final objective value (lower is better) and CPU time across different noise settings for $d=4$ . Tables report the mean $\pm$ standard error over 20 trials and 4 functions.

Figure 6: Normalized final objective value (lower is better) and CPU time across different noise settings for $d=50$ . Tables report the mean $\pm$ standard error over 20 trials and 5 functions.

Figure 7: Convergence of STREGO, TREGO, TURBO, BAXUS and NSMA-BO on six real-world benchmarks of increasing dimensionality ( $16$ d to $124$ d).

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Hyperparameter	Setting
Initial DoE size ( $N_{0}$ )	$10$
Evaluation budget	$200$
Number of trials	$20$
Base seed	$42$
Initial trust-region radius ( $\delta_{0}$ )	$0.5\,(1/5)^{1/d}$
Expansion factor ( $\gamma$ )	$2.0$

Appendix

Table 1: STREGO hyperparameters used for a

d

-dimensional problem.

Figure 8: Comparison of STREGO with global batch sizes $\mathrm{G}\in\{1,2,3,4\}$ , all other settings held fixed, across dimensions and noise settings, averaged over 20 trials.

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Apr 24, 2026J/K move · Enter open · S save

Rethinking Trust Region Bayesian Optimization in High Dimensions

Wei-Ting Tang, Joel A. Paulson

University of Wisconsin–Madison

Bayesian Optimization Black-Box Optimization Trust-Region Optimization Gaussian Process Regression

Open paper AskPDF arXiv

Trust Region Bayesian Optimization (TuRBO) is an effective strategy for alleviating the curse of dimensionality in high-dimensional black-box optimization. However, inappropriate lengthscale design can cause the local Gaussian process (GP) model within the trust region to degenerate, leading to suboptimal performance in high dimensions. In this work, we show that TuRBO's local GP may remain either excessively complex or overly simple as the dimension

D

and trust region side length

L

vary. To address this issue, we propose a straightforward variant, AdaScale-TuRBO, which scales the GP lengthscale with both the problem dimension and trust region size, thereby preserving kernel geometry and maintaining consistent prior complexity. Empirically, we show that AdaScale-TuRBO can robustly outperform standard TuRBO and other popular high-dimensional BO methods on synthetic benchmarks and real-world trajectory planning tasks.

Abstract

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