# Global optimization via inverse distance weighting and radial basis functions

arXiv: https://arxiv.org/abs/1906.06498 · HTML: https://mlsanity.com/paper/1906.06498/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2019.

## Built on by (most cited first, 16 of 16)

- [Active Learning for Regression by Inverse Distance Weighting](https://mlsanity.com/paper/2204.07177/) (2022)
- [GLISp-r: A preference-based optimization algorithm with convergence guarantees](https://mlsanity.com/paper/2202.01125/) (2022)
- [Mastering the exploration-exploitation trade-off in Bayesian Optimization](https://mlsanity.com/paper/2305.08624/) (2023)
- [Piecewise linear regression and classification](https://mlsanity.com/paper/2103.06189/) (2021)
- [Uncertainty quantification and exploration-exploitation trade-off in humans](https://mlsanity.com/paper/2102.07647/) (2021)
- [Learning Critical Scenarios in Feedback Control Systems for Automated Driving](https://mlsanity.com/paper/2209.12586/) (2022)
- [Gamifying optimization: a Wasserstein distance-based analysis of human search](https://mlsanity.com/paper/2112.06292/) (2021)
- [A unified surrogate-based scheme for black-box and preference-based optimization](https://mlsanity.com/paper/2202.01468/) (2022)
- [An active learning method for solving competitive multi-agent decision-making and control problems](https://mlsanity.com/paper/2212.12561/) (2022)
- [Global and Preference-based Optimization with Mixed Variables using Piecewise Affine Surrogates](https://mlsanity.com/paper/2302.04686/) (2023)
- [Experience in Engineering Complex Systems: Active Preference Learning with Multiple Outcomes and Certainty Levels](https://mlsanity.com/paper/2302.14630/) (2023)
- [Minimal Learning Machine for Multi-Label Learning](https://mlsanity.com/paper/2305.05518/) (2023)
- [Automatic dimensionality reduction of Twin-in-the-Loop Observers](https://mlsanity.com/paper/2401.10945/) (2024)
- [Nonmyopic Global Optimisation via Approximate Dynamic Programming](https://mlsanity.com/paper/2412.04882/) (2024)
- [Bayesian Optimization by Kernel Regression and Density-based Exploration](https://mlsanity.com/paper/2502.06178/) (2025)
- [Learning Low-Dimensional Embeddings for Black-Box Optimization](https://mlsanity.com/paper/2505.01112/) (2025)

## Abstract (arXiv)

Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the surrogate is minimum (exploitation of the surrogate) and looking for regions of the feasible space that have not yet been visited and that may potentially contain better values of the objective function (exploration of the feasible space). This paper proposes a new global optimization algorithm that uses a combination of inverse distance weighting (IDW) and radial basis functions (RBF) to construct the acquisition function. Rather arbitrary constraints that are simple to evaluate can be easily taken into account. Compared to Bayesian optimization, the proposed algorithm, that we call GLIS (GLobal minimum using Inverse distance weighting and Surrogate radial basis functions), is competitive and computationally lighter, as we show in a set of benchmark global optimization and hyperparameter tuning problems. MATLAB and Python implementations of GLIS are available at urlhttp://cse.lab.imtlucca.it/~bemporad/glis.