Reproduce “A Corrected Expected Improvement Acquisition Function Under Noisy Observations” on OpenResearch

About this paper

Han Zhou, Xingchen Ma, Matthew B Blaschko

This research introduces a corrected Expected Improvement (EI) acquisition function for Bayesian Optimization that precisely accounts for the inherent uncertainty of the incumbent solution and leverages full covariance information under noisy observations. The proposed analytical closed-form solution demonstrated improved optimization performance over standard EI on various benchmark functions and real-world machine learning tasks, while maintaining computational efficiency.

Key insights

• Treating the incumbent best solution as a deterministic value in Expected Improvement (EI) under noisy observations is a conceptual flaw that can lead to suboptimal search behavior.
• Correctly accounting for the uncertainty of the incumbent and the full covariance information from the Gaussian Process (GP) model is essential for a robust and effective EI in noisy settings.
• It is possible to derive an analytical, closed-form expression for EI that addresses incumbent uncertainty without incurring the high computational costs of Monte Carlo-based methods.

Summary by alphaXiv.