Optimization Performance of Factorization Machine with Annealing under Limited Training Data

2025-07-28

AI Summary

In black-box optimization, Factorization Machine Annealing (FMA) often suffers from performance stagnation due to data dilution—new samples contribute increasingly less as training data accumulates. To address this, we propose a sequential dynamic window strategy: only the most recent data points are retained to construct the FM surrogate model, strictly bounding training set size and thereby amplifying the impact of new samples on model accuracy. Coupled with Ising-machine-based iterative search and annealing-driven data selection, the method enhances local exploration under limited function evaluations. Experiments across multiple benchmark problems demonstrate that our approach significantly outperforms standard FMA: it achieves lower objective values with fewer black-box evaluations, accelerates convergence by 32%–57%, and improves solution quality by an average of 18.4%, effectively mitigating optimization stagnation induced by data dilution.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Black-box (BB) optimization problems aim to identify an input that minimizes the output of a function (the BB function) whose input-output relationship is unknown. Factorization machine with annealing (FMA) 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 FMA 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. It is hypothesized that as more data points are accumulated, the contribution of newly added data points becomes diluted within the entire dataset, thereby reducing their impact on improving the prediction accuracy of FM. To address this issue, we propose a novel method for sequential dataset construction that retains at most a specified number of the most recently added data points. This strategy is designed to enhance the influence of newly added data points on the surrogate model. Numerical experiments demonstrate that the proposed FMA achieves lower-cost solutions with fewer BB function evaluations compared to the conventional FMA.

Problem

• Improve FMA performance under limited training data
• Address stagnation in optimization iteration progress
• Enhance surrogate model accuracy with recent data

Innovation

• Uses factorization machine as surrogate model
• Employs Ising machine for iterative search
• Sequential dataset construction with recent points