SWIFT-FMQA: Enhancing Factorization Machine With Quadratic-Optimization Annealing via Sliding Window

Derivative-free (DF) optimization problems aim to identify an input that maximizes or minimizes the output of an objective function whose input-output relationship is unknown. Factorization machine with quadratic-optimization annealing (FMQA) is a promising approach to this task, employing a factorization machine (FM) as a surrogate model to iteratively guide the solution search via an Ising machine. Although FMQA has demonstrated strong optimization performance across various applications, its performance often stagnates as the number of optimization iterations increases. One contributing factor to this stagnation is the growing number of data points in the dataset used to train FM. As more data are accumulated, the contribution of newly added data points tends to become diluted within the entire dataset. Based on this observation, we hypothesize that such dilution reduces the impact of new data on improving the prediction accuracy of FM. To address this issue, we propose a novel method named sliding window for iterative factorization training combined with FMQA (SWIFT-FMQA). This method improves upon FMQA by utilizing a sliding-window strategy to sequentially construct a dataset that retains at most a specified number of the most recently added data points. SWIFT-FMQA is designed to enhance the influence of newly added data points on the surrogate model. Numerical experiments demonstrate that SWIFT-FMQA obtains lower-cost solutions with fewer objective function evaluations compared to FMQA.