自动调优量子启发退火机上的SVM模型,提升分类准确率。
Formulation-Level Auto-Tuning for QUBO-Based Machine Learning: A Case Study Across Multiple Quantum-Inspired Annealers
- 用Optuna自动优化编码基、核参数和惩罚项,统一调参框架。
- 在带噪数据上比传统网格搜索平均提升0.8~2.1个百分点。
- 适合研究量子启发计算与机器学习融合的开发者使用。
本文提出一种基于Optuna的公式级自动调优框架,用于在多种量子启发退火机上实现支持向量机(SVM)。在退火型SVM中,连续对偶变量被离散化并转化为无约束二次二值优化(QUBO)模型。该转换引入三类耦合参数:表示参数(编码基B和位深度K),决定数值范围、分辨率和QUBO规模;RBF核参数γ,影响分类器几何结构;等式约束惩罚ξ,控制可行性与系数平衡。将它们联合选择建模为混合离散-连续黑箱优化问题。框架包含两层优化:内层退火机最小化生成的QUBO,外层Optuna在每次试验中重构公式并最大化验证准确率。该无依赖求解器的方法应用于Fixstars Amplify Annealing Engine、Toshiba SQBM+和Fujitsu Digital Annealer,采用TPE与高斯过程采样器,对比传统网格搜索。在线性和非线性分类任务中(含0-20%标签噪声),平均准确率分别提升约0.8和2.1个百分点。结果表明,需联合评估公式质量与后端能力,任务级反馈可补偿离散化误差、惩罚失衡及后端近似优化问题。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。