Stochastic First Order Method

Stochastic first-order methods are optimization algorithms that use noisy gradient estimates to efficiently solve large-scale problems, aiming to find approximate solutions with minimal computational cost. Current research focuses on improving convergence rates and sample complexity under various conditions, including non-convexity, non-smoothness, and heavy-tailed noise, often employing techniques like variance reduction, adaptive step sizes, and proximal methods within algorithms such as AdaGrad, SGD, and their variants. These advancements are crucial for training complex machine learning models, particularly in deep learning and reinforcement learning, where high dimensionality and stochasticity are prevalent, leading to more efficient and robust model training.