Subsampling Factorization Machine Annealing

Quantum computing and machine learning are state-of-the-art technologies which have been investigated intensively in both academia and industry. The hybrid technology of these two ingredients is expected to be a powerful tool to solve complex problems in many branches of science and engineering such as combinatorial optimization problems and accelerate the creation of next-generation technologies. In this work, we develop an algorithm to solve a black-box optimization problem by improving Factorization Machine Annealing (FMA) such that the training of a machine learning model called Factorization Machine is performed not by a full dataset but by a subdataset which is sampled from a full dataset: Subsampling Factorization Machine Annealing (SFMA). According to such a probabilistic training process, the performance of FMA on exploring a solution space gets enhanced. As a result, SFMA exhibits balanced performance of exploration and exploitation which we call exploitation-exploration functionality. We conduct numerical benchmarking tests to compare the performance of SFMA with that of FMA. Consequently, SFMA certainly exhibits the exploration-exploitation functionality and outperforms FMA in speed and accuracy. In addition, the performance of SFMA can be further improved by sequentially using two subsampling datasets with different sizes such that the size of the latter dataset is substantially smaller than the former. Such a substantial reduction not only enhances the exploration performance of SFMA but also enables us to run it with correspondingly low computational cost even for a large-scale problem. These results indicate the effectiveness of SFMA in a certain class of black-box optimization problems of significant size: the potential scalability of SFMA in solving large-scale problems with correspondingly low computational cost.