INQA Conference 2025: Yusuke Hama - GQuAT, AIST

Title: Subsampling Factorization Machine Annealing

Abstract: Quantum computing (quantum annealing and gate-based quantum computing) and machine learning are state-of-the art technologies which have been extensively investigated and have the potential to accelerate industrial advancements. In recent years, the hybrid algorithm of these two ingredients so-called Factorization Machine Annealing (FMA), which is an algorithm for solving black-box combinatorial optimization problems, has been well studied from both fundamental and applied perspectives. Such a hybrid technology is expected to be a cornerstone for tackling complex optimization problems in the real-world and creating next-generation technologies for industrial developments. Toward this goal, in this work, we develop an algorithm called Subsampling Factorization Machine Annealing (SFMA) based on FMA. The main difference between FMA and SFMA is that FMA is performed by using a full dataset whereas SFMA is executed by using a subdataset which is sampled from a full dataset. Due to this probabilistic procedure, it is expected that the exploration performance is amplified and SFMA exhibits the balanced performance of exploration and exploitation: exploration-exploitation functionality. To verify the exploration-exploitation functionality and the utility of SFMA for solving various black-box combinatorial optimization problems, we perform numerical experiments using a class of black-box optimization problems called lossy compression of data matrices, which is a technique for data compression used in, for instance, image processing. These numerical experiments are conducted by benchmarking SFMA against FMA over multiple problem instances with various problem sizes (the number of spins or qubits). As a result, SFMA certainly exhibits the exploration-exploitation functionality and enables us to find the optimal solutions with faster speed and higher accuracy than FMA. Furthermore, SFMA exhibits the potential scalability in solving large-scale black-box combinatorial optimization problems with lower computational cost. We expect that SFMA has the potential to become a building block for solving various optimization problems in the real world and advance scientific research in the fields of machine learning and quantum computing.