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

2025-04-29

AI Summary

This paper addresses Bayesian optimization (BO) for highly noisy, high-variance stochastic black-box functions. We propose a trust-region-driven adaptive replication BO framework. Our method dynamically restricts the search to a local trust region and constructs a localized Gaussian process model using adaptively replicated evaluations of historical query points—thereby balancing fidelity and efficiency. Key contributions include: (1) a novel acquisition function that explicitly incorporates replication incentives, jointly modeling evaluation cost and variance-induced uncertainty; and (2) an efficient reuse strategy for prior evaluations within the trust region to enhance local model accuracy without redundant sampling. Experiments demonstrate that our approach improves optimization accuracy by 2–3 orders of magnitude over state-of-the-art methods under high-variance settings, while significantly reducing average evaluation cost. The framework exhibits strong scalability and practical deployability in real-world stochastic optimization scenarios.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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).

Problem

• Optimizing stochastic functions with high variance using trust-region Bayesian optimization
• Reducing evaluation costs while maintaining accuracy in high-throughput regimes
• Improving scaling and performance compared to existing replication methods

Innovation

• Uses Gaussian process models in trust-region framework
• Employs replication and local modeling for high variance
• Optimizes acquisition function and evaluation costs