Dual Averaging

Dual averaging is a first-order optimization method used to solve convex optimization problems, particularly those arising in machine learning and distributed systems. Current research focuses on improving the efficiency and robustness of dual averaging algorithms, including developing accelerated variants (e.g., using cyclic coordinate descent or extrapolation) and adapting them to distributed settings (e.g., federated learning and multi-agent systems with communication delays). These advancements address challenges like slow convergence in large-scale problems and the need for efficient handling of noisy or incomplete data, impacting fields ranging from quantum state tomography to real-time state estimation in cyber-physical systems. The development of variance-reduced and hierarchical approaches further enhances the scalability and practical applicability of dual averaging methods.