Iterative Stochastic

Iterative stochastic methods are computational algorithms that iteratively refine solutions using noisy, sampled data, aiming for efficient optimization or fixed-point approximation. Current research emphasizes improving convergence rates and sample efficiency through techniques like variance reduction, Markovian modeling of noise, and sketching-based dimensionality reduction within algorithms such as stochastic gradient descent, temporal difference learning, and Halpern iterations. These advancements have significant implications for diverse fields, including machine learning (federated learning, linear systems solving), image reconstruction (MRI, CT), and reinforcement learning, enabling faster and more robust solutions to complex problems.