# Knowing The What But Not The Where in Bayesian Optimization

arXiv: https://arxiv.org/abs/1905.02685 · HTML: https://mlsanity.com/paper/1905.02685/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2019.

## Built on by (most cited first, 20 of 20)

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- [High Dimensional Bayesian Optimization using Lasso Variable Selection](https://mlsanity.com/paper/2504.01743/) (2025)
- [Gaussian Process Sampling and Optimization with Approximate Upper and Lower Bounds](https://mlsanity.com/paper/2110.12087/) (2021)
- [Natural Evolutionary Search meets Probabilistic Numerics](https://mlsanity.com/paper/2507.07288/) (2025)
- [Machine Learning for Combinatorial Optimisation of Partially-Specified Problems: Regret Minimisation as a Unifying Lens](https://mlsanity.com/paper/2205.10157/) (2022)
- [Generalization within in silico screening](https://mlsanity.com/paper/2307.09379/) (2023)
- [Respecting the limit:Bayesian optimization with a bound on the optimal value](https://mlsanity.com/paper/2411.04744/) (2024)
- [Weighted Euclidean Distance Matrices over Mixed Continuous and Categorical Inputs for Gaussian Process Models](https://mlsanity.com/paper/2503.02630/) (2025)
- [HyperController: A Hyperparameter Controller for Fast and Stable Training of Reinforcement Learning Neural Networks](https://mlsanity.com/paper/2504.19382/) (2025)

## Abstract (arXiv)

Bayesian optimization has demonstrated impressive success in finding the optimum input x* and output f* = f(x*) = max f(x) of a black-box function f. In some applications, however, the optimum output f* is known in advance and the goal is to find the corresponding optimum input x*. In this paper, we consider a new setting in BO in which the knowledge of the optimum output f* is available. Our goal is to exploit the knowledge about f* to search for the input x* efficiently. To achieve this goal, we first transform the Gaussian process surrogate using the information about the optimum output. Then, we propose two acquisition functions, called confidence bound minimization and expected regret minimization. We show that our approaches work intuitively and give quantitatively better performance against standard BO methods. We demonstrate real applications in tuning a deep reinforcement learning algorithm on the CartPole problem and XGBoost on Skin Segmentation dataset in which the optimum values are publicly available.