Optimal Convergence Rate

Optimal convergence rate research focuses on achieving the fastest possible speed of convergence for various optimization algorithms used in machine learning. Current efforts center on analyzing and improving the convergence rates of stochastic gradient methods (like SGD, Adam, RMSProp), quasi-Newton methods, and algorithms tailored for federated learning and distributed settings, often considering different model architectures and loss functions (convex, non-convex, smooth, non-smooth). These advancements are crucial for improving the efficiency and scalability of machine learning models, impacting areas such as deep learning training, reinforcement learning, and privacy-preserving distributed computation. Establishing optimal rates provides theoretical benchmarks for algorithm design and guides the development of more efficient and robust machine learning systems.