通过优化初始数据设计，提升因子分解机在离散变量优化中的性能
Improving FMQA via Initial Training Data Design Considering Marginal Bit Coverage in One-Hot Encoding
- 用LHS和Sobol'序列确保每比特变量至少出现一次，避免参数无梯度更新
- 在17和32变量机翼设计任务中，平均巡航速度优于基线方法，32变量时优势更明显
- 适合需要高效探索离散空间的黑箱优化场景，如工程设计与超参数调优
因子分解机带二次优化退火（FMQA）是一种黑箱优化方法，结合因子分解机（FM）代理模型与基于QUBO的伊辛机搜索。当使用独热编码处理整数或离散化连续变量时，均匀随机初始化可能导致许多二元变量从未激活，使其对应的FM参数无法获得直接梯度更新。为此，我们设计初始训练数据以实现完整的边际比特覆盖，即确保每个独热编码产生的二元变量至少取值为1一次。采用两种空间填充采样方法：拉丁超立方采样（LHS）和Sobol'序列，分别得到LHS-FMQA与Sobol'-FMQA。在含17和32个设计变量的人力驱动飞机机翼形状优化基准测试中，两种方法均取得比基线FMQA更高的平均最终巡航速度，且在32变量问题中优势更为显著。
原文摘要 · Abstract (English)
Factorization machine with quadratic-optimization annealing (FMQA) is a black-box optimization method that combines a factorization machine (FM) surrogate with QUBO-based search by an Ising machine. When FMQA is applied to integer or discretized continuous variables via one-hot encoding, uniform random initial sampling can leave many binary variables never active in the initial training data, and the corresponding FM parameters receive no direct gradient updates from the observed responses. We address this by designing the initial training data to achieve complete marginal bit coverage, namely, ensuring that every binary variable obtained by one-hot encoding takes the value one at least once. We use two space-filling sampling methods, Latin hypercube sampling (LHS) and the Sobol' sequence, yielding LHS-FMQA and Sobol'-FMQA. On the human-powered aircraft wing-shape optimization benchmark with 17 and 32 design variables, both proposed methods achieved numerically higher mean final cruising speeds than the baseline FMQA, with the advantage more pronounced on the 32-variable problem.
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