# Efficient computation of the Knowledge Gradient for Bayesian Optimization

arXiv: https://arxiv.org/abs/2209.15367 · HTML: https://mlsanity.com/paper/2209.15367/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Multi-Information Source Optimization](https://mlsanity.com/paper/1603.00389/) (2016)
- [Bayesian Optimization with Gradients](https://mlsanity.com/paper/1703.04389/) (2017)
- [Bayesian Optimization Allowing for Common Random Numbers](https://mlsanity.com/paper/1910.09259/) (2019)
- [Discretization-free Knowledge Gradient Methods for Bayesian Optimization](https://mlsanity.com/paper/1707.06541/) (2017)

## Built on by (most cited first, 4 of 4)

- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)
- [Multi-fidelity batch Bayesian optimization for bioprocess development across scales](https://mlsanity.com/paper/2508.10970/) (2025)
- [Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems](https://mlsanity.com/paper/2408.17387/) (2024)
- [Fast Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2506.11456/) (2025)

## Abstract (arXiv)

Bayesian optimization is a powerful collection of methods for optimizing stochastic expensive black box functions. One key component of a Bayesian optimization algorithm is the acquisition function that determines which solution should be evaluated in every iteration. A popular and very effective choice is the Knowledge Gradient acquisition function, however there is no analytical way to compute it. Several different implementations make different approximations. In this paper, we review and compare the spectrum of Knowledge Gradient implementations and propose One-shot Hybrid KG, a new approach that combines several of the previously proposed ideas and is cheap to compute as well as powerful and efficient. We prove the new method preserves theoretical properties of previous methods and empirically show the drastically reduced computational overhead with equal or improved performance. All experiments are implemented in BOTorch and code is available on github.