Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functions

TL;DR

This work tackles stochastic, high-variance optimization by marrying trust-region strategies with Gaussian-process surrogates and a systematic replication mechanism. It introduces a novel infill criterion, qERCI, and an adaptive joint selection of the next point and replication budget, enabling effective look-ahead under setup costs. Key contributions include local GP modeling within trust regions, a robust acceptance test, a variance-based rule to stabilize radius adjustments, and cost-aware variants that balance replication with forward-looking gains. Empirical results show substantial gains in accuracy and speed over existing GP-TR and global BO methods, especially in noisy or setup-cost scenarios, highlighting practical impact for expensive, high-variance optimization tasks.

Abstract

We develop and analyze a method for stochastic simulation optimization relying on Gaussian process models within a trust-region framework. We are interested in the case when the variance of the objective function is large. We propose to rely on replication and local modeling to cope with this high-throughput regime, where the number of evaluations may become large to get accurate results while still keeping good performance. We propose several schemes to encourage replication, from the choice of the acquisition function to setup evaluation costs. Compared with existing methods, our results indicate good scaling, in terms of both accuracy (several orders of magnitude better than existing methods) and speed (taking into account evaluation costs).

Figures (6)

• Figure 1: GP models and the KG and EQI infill criteria, depending on the number of replicates ($p$) at the future points, for two cases (left and right). Vertical lines indicate design points.
• Figure 2: Parallel reduction in improvement example for the cases in \ref{['fig:GPandcrits']}, one case per column. Crosses mark the respective maxima. Top: qERCI for one new point $\mathbf{x}_{n+1}$ allowing for various numbers of replicates ($p$). Bottom: qERCI for two new points. The dashed line marks where $\mathbf{x}_{n+1}=\mathbf{x}_{n+2}$.
• Figure 3: Gaussian processes with various $\mathbb{V}\left[{m_n(X)}\right]$ vs. $\mathbb{E}[s_n^2(X)]$ ratios.
• Figure 4: Data profiles of the method against TuRBO and BoTorch on Benchmark 1.
• Figure 5: Data profiles of the method against TuRBO and BoTorch on Benchmark 2.