Formulation-Level Auto-Tuning for QUBO-Based Machine Learning: A Case Study Across Multiple Quantum-Inspired Annealers

2026-07-21

AI Summary

This work addresses the challenges of parameter coupling and tuning difficulty arising from discretization when solving support vector machines formulated as QUBO problems on quantum-inspired annealers. To overcome these issues, the authors propose a two-level automated tuning framework based on Optuna: the inner loop solves the QUBO using the annealer, while the outer loop dynamically reconstructs the QUBO and optimizes validation accuracy by jointly adjusting the encoding basis, bit depth, kernel hyperparameters, and constraint penalty coefficients. For the first time, representation parameters, learning hyperparameters, and penalty terms are unified into a mixed discrete–continuous black-box optimization problem, enabling solver-agnostic auto-tuning across platforms such as Fixstars Amplify, Toshiba SQBM+, and Fujitsu Digital Annealer. On linear and nonlinear classification tasks with 0–20% label noise, the method improves average accuracy by 0.8 and 2.1 percentage points over grid search, demonstrating that task-driven feedback effectively compensates for discretization and hardware approximation errors.

Abstract

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.

Problem

• QUBO
• quantum-inspired annealing
• parameter tuning
• SVM
• discretization

Innovation

• QUBO formulation
• formulation-level auto-tuning
• quantum-inspired annealing
• mixed discrete-continuous optimization
• solver-agnostic framework