AI 中文总结
研究基于QUBO的机器学习公式级自动调优，通过Optuna框架解决多量子启发退火器上SVM参数联合选择问题，有内外两个优化级别，经实验对比传统网格搜索，在分类任务中平均增益显著，表明要联合评估公式与后端能力。
AI 中文摘要
本文提出了一个基于Optuna的公式级自动调优框架，用于在多个量子启发退火器上实现的支持向量机（SVM）。在基于退火的SVM中，连续对偶变量被离散化并转换为二次无约束二元优化（QUBO）模型。这种转换引入了三类耦合参数：表示参数（编码基数B和比特深度K）、RBF核参数γ和平等约束惩罚ξ。我们将它们的联合选择公式化为一个混合离散-连续黑箱优化问题。该框架有两个优化级别：内部退火器最小化生成的QUBO，而外部Optuna循环在每次试验中重建公式并最大化验证准确率。使用TPE和高斯过程采样器将相同的与求解器无关的过程应用于Fixstars Amplify退火引擎、东芝SQBM+和富士通数字退火器，并与传统网格搜索进行比较。在有0-20%标签噪声的线性和非线性分类任务上的实验表明，相对于网格搜索，平均增益分别约为0.8和2.1个百分点。结果表明，必须联合评估公式质量和后端能力，并且任务级反馈可以补偿离散化、惩罚不平衡和后端相关的近似优化。
英文摘要
This paper presents an Optuna-based formulation-level auto-tuning framework for support vector machines (SVMs) implemented on multiple quantum-inspired annealers. In an annealing-based SVM, continuous dual variables are discretized and converted into a quadratic unconstrained binary optimization (QUBO) model. This transformation introduces three coupled classes of parameters: representation parameters-the encoding base B and bit depth K-which determine numerical range, resolution, and QUBO size; the RBF kernel parameter γ, which determines classifier geometry; and the equality-constraint penalty ξ, which controls feasibility and coefficient balance. We formulate their joint selection as a mixed discrete-continuous black-box optimization problem. The framework has two optimization levels: an inner annealer minimizes the generated QUBO, while an outer Optuna loop reconstructs the formulation in every trial and maximizes validation accuracy. The same solver-agnostic procedure is applied to Fixstars Amplify Annealing Engine, Toshiba SQBM+, and Fujitsu Digital Annealer using TPE and Gaussian-process samplers and is compared with conventional grid search. Experiments on linear and nonlinear classification tasks with 0-20% label noise show mean gains over grid search of approximately 0.8 and 2.1 percentage points, respectively. The results demonstrate that formulation quality and backend capability must be evaluated jointly and that task-level feedback can compensate for discretization, penalty imbalance, and backend-dependent approximate optimization.
