New q-Gradient Method Improves Machine Learning Optimization

Researchers have introduced a new optimization framework designed to address the instability and hyperparameter sensitivity often observed in standard gradient descent algorithms. The study, published in Multimedia Tools and Applications, presents a method called Variable Jackson q-Gradient Descent (VJqGD), which utilizes concepts from Jackson q-calculus to improve the training process for machine learning models.

The core innovation of the VJqGD framework is its use of an exponentially annealed schedule for the deformation parameter, denoted as q. This mathematical formulation provides researchers with explicit control over the initial magnitude of the deformation and the rate at which the algorithm transitions toward the classical gradient regime.

The authors derived theoretical properties for the underlying Jackson q-gradient method to establish its mathematical validity. Under standard smoothness assumptions, the study demonstrates that the method converges to a stationary point. Furthermore, the researchers established an O(1/T) convergence-rate bound for the minimum squared q-gradient norm. Under more stringent conditions regarding the q-deformation, the analysis achieved additional convergence rates along with logarithmic iteration complexities.

To evaluate the practical performance of VJqGD, the team conducted an experimental analysis on four benchmark supervised classification datasets from the UCI repository. The datasets selected for this evaluation were Arrhythmia, Fertility, Pima Indians Diabetes, and SPECT Heart. The experimental protocol was designed to ensure a fair comparison by using an identical setup for all tested optimizers. This included the same single-layer model architecture, the same learning-rate tuning procedure, and a fixed training budget of 50 epochs.

The performance of VJqGD was compared against seven widely used optimization algorithms: SGD, Adam, RMSprop, AdamW, AdaBelief, Lion, and Sophia. The evaluation metrics included accuracy, Macro-F1, balanced accuracy, and AUC-ROC. In the noise-free setting, VJqGD achieved the highest or tied-highest accuracy on all four benchmark datasets. Its peak performance was observed on the Fertility dataset, where it reached an accuracy of 0.8700.

Beyond overall accuracy, the method demonstrated specific strengths in other performance metrics. VJqGD attained the best Macro-F1 score on the Arrhythmia dataset, recording a value of 0.3981. It also achieved the best balanced accuracy on the Fertility dataset, with a score of 0.4947. Additionally, the method produced an AUC-ROC of 0.8345 on the Pima Indians Diabetes dataset.

The study also investigated the robustness of the proposed method under noisy conditions. When 10% label noise was introduced into the datasets, VJqGD maintained competitive performance relative to the other optimizers.

Subject of Research: Development and evaluation of a Variable Jackson q-Gradient Descent method for machine learning optimization

Article Title: Enhancing machine learning optimization using an improved q-gradient descent method

Article References: Razzouki, O. F., Charroud, A., Allali, Z. E., & Chetouani, A. (2026). Enhancing machine learning optimization using an improved q-gradient descent method. Multimedia Tools and Applications, 85(11), Article 841. https://doi.org/10.1007/s11042-026-21985-1

Image Credits: AI Generated

DOI: 10.1007/s11042-026-21985-1

Keywords: machine learning, optimization, gradient descent, q-calculus, VJqGD, classification, UCI repository, convergence, hyperparameters, algorithm, Enhancing, machine