# Active learning for enumerating local minima based on Gaussian process derivatives

arXiv: https://arxiv.org/abs/1903.03279 · HTML: https://mlsanity.com/paper/1903.03279/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2019.

## Built on by (most cited first, 3 of 3)

- [Active learning for distributionally robust level-set estimation](https://mlsanity.com/paper/2102.04000/) (2021)
- [Adaptive Defective Area Identification in Material Surface Using Active Transfer Learning-based Level Set Estimation](https://mlsanity.com/paper/2304.01404/) (2023)
- [Active Learning for Abrupt Shifts Change-point Detection via Derivative-Aware Gaussian Processes](https://mlsanity.com/paper/2312.03176/) (2023)

## Abstract (arXiv)

We study active learning (AL) based on Gaussian Processes (GPs) for efficiently enumerating all of the local minimum solutions of a black-box function. This problem is challenging due to the fact that local solutions are characterized by their zero gradient and positive-definite Hessian properties, but those derivatives cannot be directly observed. We propose a new AL method in which the input points are sequentially selected such that the confidence intervals of the GP derivatives are effectively updated for enumerating local minimum solutions. We theoretically analyze the proposed method and demonstrate its usefulness through numerical experiments.