Black-box optimization (BBO) can be used to optimize functions whose analytic form is unknown. A common approach to realising BBO is to learn a surrogate model which approximates the target black-box function which can then be solved via white-box optimization methods. In this paper, we present our approach BOX-QUBO, where the surrogate model is a QUBO matrix. However, unlike in previous state-of-the-art approaches, this matrix is not trained entirely by regression, but mostly by classification between 'good' and 'bad' solutions. This better accounts for the low capacity of the QUBO matrix, resulting in significantly better solutions overall. We tested our approach against the state-of-the-art on four domains and in all of them BOX-QUBO showed better results. A second contribution of this paper is the idea to also solve white-box problems, i.e. problems which could be directly formulated as QUBO, by means of black-box optimization in order to reduce the size of the QUBOs to the information-theoretic minimum. Experiments show that this significantly improves the results for MAX-k-SAT.

翻译：黑箱优化可用于优化解析形式未知的函数。实现黑箱优化的常见方法是学习一个近似目标黑箱函数的代理模型，随后可通过白箱优化方法求解。本文提出了BOX-QUBO方法，其中代理模型是一个QUBO矩阵。与现有最优方法不同，该矩阵并非完全通过回归训练，而是主要基于对"优"解与"劣"解的分类训练。这种方法更好地适应了QUBO矩阵的低容量特性，从而整体上获得了显著更优的解。我们在四个领域与现有最优方法进行了对比测试，BOX-QUBO在所有领域均表现更优。本文的第二个贡献在于提出将白箱问题（即可直接表述为QUBO的问题）通过黑箱优化方法求解，从而将QUBO的规模缩减至信息论最小值。实验表明，该方法显著提升了MAX-k-SAT问题的求解结果。