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This paper introduces an Optuna-based framework for formulation-level auto-tuning of support vector machines (SVMs) on various quantum-inspired annealers, addressing the complexities of parameter selection in the QUBO model. By treating the joint selection of representation parameters, RBF kernel parameters, and equality-constraint penalties as a mixed discrete-continuous optimization problem, the framework optimizes both the generated QUBO and validation accuracy. The results indicate that this approach outperforms conventional grid search, achieving mean accuracy gains of approximately 0.8 and 2.1 percentage points for linear and nonlinear classification tasks, respectively, highlighting the importance of joint evaluation of formulation quality and backend capabilities.
Achieving up to 2.1 percentage points improvement in classification accuracy by optimizing SVM formulations across multiple quantum-inspired annealers reveals the critical interplay between parameter selection and backend performance.
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 {\gamma}, which determines classifier geometry; and the equality-constraint penalty {\xi}, 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.
