Hybrid Quantum-Classical Algorithm for an Integrated Feature Selection and Logistic Regression Model

Feature selection is a pivotal step in machine learning, aimed at reducing feature dimensionality and improving model performance. Conventional feature selection methods, typically framed as NP-hard problems, focus primarily on selecting nonredundant and discriminative features but neglect how these selected features influence downstream machine learning tasks. To bridge this gap, we propose a mixed-integer nonlinear programming-based integrated feature selection and logistic regression (IFSLR) model that jointly optimizes feature selection and classifier parameters. To solve the proposed IFSLR model efficiently, we reformulate it into two quantum-computing-compatible quadratic unconstrained binary optimization (QUBO) models via discretization of continuous variables and Taylor expansions, and provide a theoretical approximation guarantee for the proposed QUBO models. To adaptively optimize both the discretization step length optimization sub-problems and the parameterized QUBO sub-problems, we develop a dual-level Q-learning-guided hybrid quantum-classical algorithm that dynamically selects which sub-problem to solve. At the upper level, an adaptive Q-learning agent is employed to select appropriate sub-problems during the search process. At the lower level, each iteration addresses either discretization step length optimization sub-problems or parameterized QUBO sub-problems. Experiments on the German credit dataset demonstrate that our method achieves a 10.83% improvement in accuracy and a 4.54-fold enhancement in computational efficiency on average compared with state-of-the-art methods. It also achieves F₁-score improvements of 2.86% on the Wisconsin diagnostic breast cancer dataset and 7.65% on the Portuguese bank marketing dataset. The improvements further validate the effectiveness and generalizability of the proposed model and algorithm.