Modernizing HEBO: a robust Bayesian optimization baseline for practical heteroskedastic and non-stationary problems

Jul 16, 2026

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Bayesian optimization enables data-efficient sequential experiments, yet its effectiveness depends on whether surrogate-model assumptions match the objective’s geometry and noise behavior. The document presents tidyHEBO, a robust Bayesian optimization model inspired by heteroskedastic evolutionary Bayesian optimization (HEBO) for single-objective optimization. It updates surrogate training, output-warping selection, acquisition evaluation, and Pareto-front search in BoTorch. Benchmarks on synthetic functions, Olympus emulators, experimental reaction datasets, NIAH materials tasks, and Bayesmark HPO show competitive or superior performance and improved robustness across repeated runs.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages24

Reading Time1 h 0 min

Abstract

Introduction

Bayesian optimization and scientific applications

Gaussian processes: homoskedastic noise and stationarity assumptions

HEBO and motivation for a more general baseline

Proposed method: tidyHEBO

Contributions and expected improvements

Modernizing HEBO: a robust Bayesian optimization baseline for practical heteroskedastic and non-stationary problems Zhukov L.A. 1,2 , Shaburova E.V.2 , Antonets D.V. 1,2 1 AI Center MSU, Lomonosov Moscow State University, Moscow, Russia 2 MSU Institute for Artificial Intelligence, Lomonosov Moscow State University, Moscow, Russia Abstract Bayesian optimization is increasingly used to guide data-efficient experimentation in chemistry, materials science, and related laboratory settings, but its practical performance depends strongly on how well surrogate-model assumptions match the geometry and noise structure of the underlying objective. We introduce tidyHEBO, a robust Bayesian optimization model inspired by heteroskedastic evolutionary Bayesian optimization (HEBO) for single-objective, sequential optimization. tidyHEBO reconstructs the HEBO design philosophy in BoTorch and revises surrogate training, output-warping selection, acquisition function evaluation, and Pareto-front search. We benchmarked tidyHEBO on synthetic functions, Olympus emulators, fully experimental reaction-optimization datasets, needle-in-a-haystack (NIAH) materials problems, and Bayesmark hyperparameter optimization tasks. On these tasks tidyHEBO achieved competitive to superior performance and improvement in robustness across repeated optimization runs. We therefore propose tidyHEBO as a practical tool for sequential experimentations and a strong general-purpose benchmark for future Bayesian optimization research. Introduction Bayesian optimization (BO) is a sample-efficient strategy for optimizing expensive blackbox objectives by using a probabilistic surrogate model to approximate the objective function and an acquisition function (AF) to select the most informative next evaluation point. BO has proved valuable in accelerating materials discovery [1,2], drug discovery [3], reaction and catalyst optimization [4,5], and even tuning particle accelerators [6] . In these contexts, BO accelerated research, generated solutions comparable in quality to those proposed by domain experts [4] and identified novel, high-performing solutions that elude human intuition [7] . As a result, the adoption of BO in scientific experimental tasks has become a rapidly growing area of research. Despite these successes, practical BO performance is often limited by a mismatch between modeling assumptions and scientific objective landscapes. The canonical surrogate model in BO, a Gaussian process (GP), typically assumes homoskedastic observation noise. Heteroskedasticity denotes a violation of the constant-noise assumption, where the variance of the observation noise changes systematically with the location in the design space or with the magnitude of the measured quantity. Relative measurements typically induce heteroskedastic errors [8,9] . Notably, in quantitative NMR spectroscopy, a classical method for assessing reaction yields and selectivity, measurement uncertainty exhibits a pronounced nonlinear dependence on the analyte concentration [10] . Heteroskedasticity compromises the accuracy of uncertainty estimates produced by a GP (Figure 1a, b), and therefore degrades the efficiency of the optimization process [11,12] . Another common assumption when using GPs is stationarity of the kernel function. Nonstationarity occurs when the optimization objective function’s properties shift between distinct regions of the design space. Because the behavior of non-stationary objectives is not consistent across the design space, patterns learned from one region during optimization become unreliable for prediction in unseen areas, for example, when function values change rapidly in one region of the design space while another region is relatively flat [13,14] (Figure 1c, d) . In the natural sciences, non-stationary functions arise, for example, in longitudinal studies, where the target variable changes rapidly only near a specific event [15], or in flow-reactors where ev

FAQs

What problem does tidyHEBO address in Bayesian optimization?

It targets practical failures caused by surrogates mismatch, especially when objective noise is heteroskedastic and when kernel assumptions like stationarity do not hold.

How is tidyHEBO derived from HEBO?

tidyHEBO reconstructs the HEBO design philosophy using BoTorch, while revising details including surrogate training, output-warping selection, acquisition function evaluation, and Pareto-front search.

On which benchmarks does tidyHEBO get evaluated and what outcome is reported?

It is benchmarked on synthetic functions, Olympus emulators, fully experimental reaction-optimization datasets, NIAH materials problems, and Bayesmark hyperparameter optimization tasks, where it achieves competitive to superior performance and better robustness across repeated runs.

Jul 16, 2026

Upload by Riley