Mirror Prox

Mirror prox methods are a class of optimization algorithms used to solve saddle-point problems, particularly relevant in machine learning applications like federated learning and distributionally robust optimization. Current research focuses on improving the efficiency and robustness of these methods, particularly by addressing challenges related to inexact proximal updates and communication overhead in distributed settings, often employing techniques like extrapolation and kernel methods. These advancements enhance the applicability of mirror prox to large-scale problems involving high-dimensional data or distributed computation, leading to improved convergence rates and reduced computational costs.