A Universally Optimal Multistage Accelerated Stochastic Gradient Method
This work provides a universally optimal method for stochastic optimization, addressing a key challenge in machine learning and optimization, though it appears incremental as it builds on Nesterov's method.
The paper tackles the problem of minimizing a strongly convex, smooth function with noisy gradient estimates by proposing a multistage accelerated algorithm that achieves optimal convergence rates in both deterministic and stochastic settings without requiring knowledge of noise characteristics.
We study the problem of minimizing a strongly convex, smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal rate both in the deterministic and stochastic case and operates without knowledge of noise characteristics. The algorithm consists of stages that use a stochastic version of Nesterov's method with a specific restart and parameters selected to achieve the fastest reduction in the bias-variance terms in the convergence rate bounds.