Gradient Difference

Gradient difference, the variation in gradients between successive optimization steps, is a key focus in improving the efficiency and performance of optimization algorithms. Current research explores its use in adaptive optimization methods, developing novel preconditioning matrices and step-size strategies that leverage gradient differences to approximate Hessian information and dynamically adjust optimization behavior. This leads to improved convergence rates and generalization performance in various machine learning tasks, particularly in deep learning, and also offers advantages in differential privacy settings by enabling the construction of low-variance gradient estimators. The resulting algorithms show promise for enhancing the accuracy and efficiency of optimization across diverse applications.