This paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as “this is better than that” between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. A radial-basis function surrogate is fit via linear or quadratic programming, satisfying if possible the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is competitive in that, within the same number of comparisons, it usually approaches the global optimum more closely and is computationally lighter. Applications of the proposed algorithm to solve a set of benchmark global optimization problems, for multi-objective optimization, and for optimal tuning of a cost-sensitive neural network classifier for object recognition from images are described in the paper. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/glis.

本文提出了一种解决优化问题的方法，决策者无法评估目标函数，而只能表达偏好例如两个候选决策向量之间的“比这更好”。本文所述的算法旨在通过主动从过去采样的决策向量和成对偏好中学习潜在（未知且可能无法量化）目标函数的替代方法，通过迭代地提议决策者进行新的比较来达到全局优化器的目的。通过线性或二次编程拟合径向基函数替代，如果可能的话，满足决策者对现有样本表示的偏好。该代理用于根据两个可能的标准提出决策向量的新样本，以便与当前最佳候选者进行比较：最小化代理人和逆权重距离函数的组合，以在代理人的利用与决策空间探索之间取得平衡，或使与新候选人会被优先考虑的概率有关的函数最大化。与基于贝叶斯优化的主动偏好学习相比，我们证明了我们的方法具有竞争力，因为在相同数量的比较中，它通常更接近全局最优且计算更轻。本文介绍了该算法在解决一组基准全局优化问题，多目标优化以及优化成本敏感型神经网络分类器以从图像识别对象中的应用。