A Universally Optimal Multistage Accelerated Stochastic Gradient Method

TL;DR

This paper introduces a multistage accelerated stochastic gradient method that achieves optimal convergence rates in both deterministic and stochastic settings without prior noise knowledge.

Contribution

A novel multistage accelerated algorithm that is universally optimal, combining stochastic Nesterov's method with specific restarts and parameter tuning.

Findings

Achieves optimal convergence rates in both deterministic and stochastic cases.

Operates without prior knowledge of noise characteristics.

Uses staged stochastic Nesterov's method with tailored restarts.

Abstract

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.