# A unified surrogate-based scheme for black-box and preference-based optimization

arXiv: https://arxiv.org/abs/2202.01468 · HTML: https://mlsanity.com/paper/2202.01468/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 34 references that are in the map.
- First posted on arXiv 3 Feb 2022.

## Builds on (most cited first, 6 of 6)

- [A Literature Survey of Benchmark Functions For Global Optimization Problems](https://mlsanity.com/paper/1308.4008/) (2013)
- [Preferential Bayesian Optimization](https://mlsanity.com/paper/1704.03651/) (2017)
- [Preferential Bayesian optimisation with Skew Gaussian Processes](https://mlsanity.com/paper/2008.06677/) (2020)
- [Global optimization via inverse distance weighting and radial basis functions](https://mlsanity.com/paper/1906.06498/) (2019)
- [A General Stochastic Algorithmic Framework for Minimizing Expensive Black Box Objective Functions Based on Surrogate Models and Sensitivity Analysis](https://mlsanity.com/paper/1410.6271/) (2014)
- [GLISp-r: A preference-based optimization algorithm with convergence guarantees](https://mlsanity.com/paper/2202.01125/) (2022)

## Abstract (arXiv)

Black-box and preference-based optimization algorithms are global optimization procedures that aim to find the global solutions of an optimization problem using, respectively, the least amount of function evaluations or sample comparisons as possible. In the black-box case, the analytical expression of the objective function is unknown and it can only be evaluated through a (costly) computer simulation or an experiment. In the preference-based case, the objective function is still unknown but it corresponds to the subjective criterion of an individual. So, it is not possible to quantify such criterion in a reliable and consistent way. Therefore, preference-based optimization algorithms seek global solutions using only comparisons between couples of different samples, for which a human decision-maker indicates which of the two is preferred. Quite often, the black-box and preference-based frameworks are covered separately and are handled using different techniques. In this paper, we show that black-box and preference-based optimization problems are closely related and can be solved using the same family of approaches, namely surrogate-based methods. Moreover, we propose the generalized Metric Response Surface (gMRS) algorithm, an optimization scheme that is a generalization of the popular MSRS framework. Finally, we provide a convergence proof for the proposed optimization method.