# Parallel Bayesian Global Optimization of Expensive Functions

arXiv: https://arxiv.org/abs/1602.05149 · HTML: https://mlsanity.com/paper/1602.05149/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2016.

## Built on by (most cited first, 30 of 44)

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- [Batch Bayesian Optimization on Permutations using the Acquisition Weighted Kernel](https://mlsanity.com/paper/2102.13382/) (2021)
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- [Sampling from Gaussian Processes: A Tutorial and Applications in Global Sensitivity Analysis and Optimization](https://mlsanity.com/paper/2507.14746/) (2025)
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- [Batch Bayesian Optimization via Particle Gradient Flows](https://mlsanity.com/paper/2209.04722/) (2022)
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- [DASH: Decoupled Adaptive Surrogate - Acquisition Harness for Automated Bayesian Optimization](https://mlsanity.com/paper/2608.00641/) (2026)

## Abstract (arXiv)

We consider parallel global optimization of derivative-free expensive-to-evaluate functions, and propose an efficient method based on stochastic approximation for implementing a conceptual Bayesian optimization algorithm proposed by Ginsbourger et al. (2007). At the heart of this algorithm is maximizing the information criterion called the "multi-points expected improvement'', or the q-EI. To accomplish this, we use infinitessimal perturbation analysis (IPA) to construct a stochastic gradient estimator and show that this estimator is unbiased. We also show that the stochastic gradient ascent algorithm using the constructed gradient estimator converges to a stationary point of the q-EI surface, and therefore, as the number of multiple starts of the gradient ascent algorithm and the number of steps for each start grow large, the one-step Bayes optimal set of points is recovered. We show in numerical experiments that our method for maximizing the q-EI is faster than methods based on closed-form evaluation using high-dimensional integration, when considering many parallel function evaluations, and is comparable in speed when considering few. We also show that the resulting one-step Bayes optimal algorithm for parallel global optimization finds high-quality solutions with fewer evaluations than a heuristic based on approximately maximizing the q-EI. A high-quality open source implementation of this algorithm is available in the open source Metrics Optimization Engine (MOE).