Principled Design of Expected Improvement for Continuous Simulation Optimization
Abstract
Expected improvement based on stochastic kriging (SK) surrogate is widely used in continuous simulation optimization, but unknown heteroscedastic noise makes three basic design choices consequential: the incumbent to define improvement, replication allocation, and final recommendation. Existing methods typically either assume the noise levels are known or choose these components separately through heuristic rules or empirical calibration. We instead derive a high-probability upper bound on the simple regret and systematically choose the three components within general rule classes to tighten this bound. We first establish a finite-sample confidence bound for the SK predictor as a foundation for the three design choices. Within general posterior-quantile rule classes, tightening the regret certificate selects a lower-quantile incumbent and an upper-quantile recommendation among sampled designs. The opposing quantiles reflect the different roles of exploratory experiments and the final implemented decision. Under mild conditions satisfied by common kernels, minimizing a tractable kernel-specific bound yields a logarithmic replication order. Based on these design choices, the resulting simple regret matches the existing results under known homoscedastic noise up to logarithmic factors. To our knowledge, this is the first simple-regret guarantee of this form for a continuous-domain EI-type simulation optimization method that learns unknown heteroscedastic variances through replications.
Related
- Simple-regret rates and minimax optimality of fixed-prior expected improvement in Matérn and squared-exponential RKHSs
- Expected Hypervolume Maximization for Multiobjective Optimization under Uncertainties
- Scalable Discrete-to-Continuous Channel Simulation for Compression and Privacy
- Discussion on "Principled type I error rate inflation in two-arm clinical trial designs with external control information borrowing" by Silvia Calderazzo, Manuel Wiesenfarth, Vivienn Weru, and Annette Kopp-Schneider
- Steepest Guidance: A Practical and Principled Approach to Inference-Time Alignment of Flow and Diffusion-based Models
BibTeX
@misc{wang2026principled,
title = {{Principled Design of Expected Improvement for Continuous Simulation Optimization}},
author = {Songhao Wang and Jianglin Xia and Haowei Wang and Szu Hui Ng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18434},
eprint = {2610.18434},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18434},
}
RIS
TY - UNPB
TI - Principled Design of Expected Improvement for Continuous Simulation Optimization
AU - Songhao Wang
AU - Jianglin Xia
AU - Haowei Wang
AU - Szu Hui Ng
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.18434
UR - https://arxiv.org/abs/2610.18434
AB - Expected improvement based on stochastic kriging (SK) surrogate is widely used in continuous simulation optimization, but unknown heteroscedastic noise makes three basic design choices consequential: the incumbent to define improvement, replication allocation, and final recommendation. Existing methods typically either assume the noise levels are known or choose these components separately through heuristic rules or empirical calibration. We instead derive a high-probability upper bound on the simple regret and systematically choose the three components within general rule classes to tighten this bound. We first establish a finite-sample confidence bound for the SK predictor as a foundation for the three design choices. Within general posterior-quantile rule classes, tightening the regret certificate selects a lower-quantile incumbent and an upper-quantile recommendation among sampled designs. The opposing quantiles reflect the different roles of exploratory experiments and the final implemented decision. Under mild conditions satisfied by common kernels, minimizing a tractable kernel-specific bound yields a logarithmic replication order. Based on these design choices, the resulting simple regret matches the existing results under known homoscedastic noise up to logarithmic factors. To our knowledge, this is the first simple-regret guarantee of this form for a continuous-domain EI-type simulation optimization method that learns unknown heteroscedastic variances through replications.
ER -