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：黑盒优化（BBO）可用于优化解析形式未知的函数。实现BBO的一种常见方法是学习一个替代模型，该模型近似目标黑盒函数，进而可通过白盒优化方法求解。本文提出BOX-QUBO方法，其中替代模型为QUBO矩阵。然而，与先前最先进方法不同，该矩阵并非完全通过回归训练，而主要通过"好"与"坏"解的分类进行训练。这更好地适应了QUBO矩阵的低容量特性，从而在整体上获得显著更优的解。我们在四个领域将本方法对照最先进方法进行测试，BOX-QUBO在所有领域均显示更优结果。本文的第二项贡献是提出通过黑盒优化求解白盒问题（即可直接表述为QUBO的问题），以将QUBO规模压缩至信息论最小化的思路。实验表明，该方法能显著提升MAX-k-SAT问题的求解效果。