Linear Convergence Rate

Linear convergence rate, in the context of optimization algorithms, refers to the speed at which an algorithm approaches a solution, specifically achieving a reduction in error by a constant factor at each iteration. Current research focuses on achieving linear convergence in various settings, including federated learning (with architectures like multi-tier models), optimal transport problems (using algorithms like Sinkhorn-Newton), and distributed optimization (employing methods such as heavy ball and accelerated gradient descent). These advancements are significant because faster convergence translates to reduced computational costs and improved efficiency in diverse machine learning applications, from personalized recommendations to large-scale model training.