NOSTRA: A noise-resilient and sparse data framework for trust region based multi objective Bayesian optimization

TL;DR

NOSTRA is a novel framework for multi-objective Bayesian optimization that effectively handles noisy, sparse, and scarce data by leveraging prior knowledge and trust regions to improve convergence and data efficiency.

Contribution

NOSTRA introduces a trust region-based sampling framework that incorporates prior uncertainty knowledge to enhance surrogate modeling and optimization in challenging data scenarios.

Findings

Outperforms existing methods in noisy, sparse, and scarce data conditions.

Accelerates convergence to the Pareto frontier with fewer samples.

Improves solution quality by focusing on promising regions.

Abstract

Multi-objective Bayesian optimization (MOBO) struggles with sparse (non-space-filling), scarce (limited observations) datasets affected by experimental uncertainty, where identical inputs can yield varying outputs. These challenges are common in physical and simulation experiments (e.g., randomized medical trials and, molecular dynamics simulations) and are therefore incompatible with conventional MOBO methods. As a result, experimental resources are inefficiently allocated, leading to suboptimal designs. To address this challenge, we introduce NOSTRA (Noisy and Sparse Data Trust Region-based Optimization Algorithm), a novel sampling framework that integrates prior knowledge of experimental uncertainty to construct more accurate surrogate models while employing trust regions to focus sampling on promising areas of the design space. By strategically leveraging prior information and refining search regions, NOSTRA accelerates convergence to the Pareto frontier, enhances data efficiency, and improves solution quality. Through two test functions with varying levels of experimental uncertainty, we demonstrate that NOSTRA outperforms existing methods in handling noisy, sparse, and scarce data. Specifically, we illustrate that, NOSTRA effectively prioritizes regions where samples enhance the accuracy of the identified Pareto frontier, offering a resource-efficient algorithm that is practical in scenarios with limited experimental budgets while ensuring efficient performance.