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

TL;DR

This paper introduces a unified surrogate-based optimization approach that effectively addresses both black-box and preference-based problems, demonstrating a generalized algorithm with proven convergence.

Contribution

It proposes the gMRS algorithm, unifying black-box and preference-based optimization within a surrogate modeling framework, and provides theoretical convergence guarantees.

Findings

gMRS outperforms existing methods in benchmark tests

Unified approach reduces complexity by handling both problem types

Convergence proof ensures reliability of the method

Abstract

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.