Enhancing Stochastic Optimization for Statistical Efficiency Using ROOT-SGD with Diminishing Stepsize

TL;DR

This paper improves the ROOT-SGD stochastic optimization method by incorporating a diminishing stepsize, achieving optimal convergence rates and enhanced statistical efficiency with theoretical guarantees and practical benefits.

Contribution

It introduces a diminishing stepsize strategy for ROOT-SGD, providing the first rigorous analysis of its statistical efficiency and convergence properties.

Findings

Achieves optimal convergence rates.

Provides robust theoretical guarantees.

Enhances stability and precision in optimization.

Abstract

In this paper, we revisit \textsf{ROOT-SGD}, an innovative method for stochastic optimization to bridge the gap between stochastic optimization and statistical efficiency. The proposed method enhances the performance and reliability of \textsf{ROOT-SGD} by integrating a carefully designed \emph{diminishing stepsize strategy}. This approach addresses key challenges in optimization, providing robust theoretical guarantees and practical benefits. Our analysis demonstrates that \textsf{ROOT-SGD} with diminishing achieves optimal convergence rates while maintaining computational efficiency. By dynamically adjusting the learning rate, \textsf{ROOT-SGD} ensures improved stability and precision throughout the optimization process. The findings of this study offer valuable insights for developing advanced optimization algorithms that are both efficient and statistically robust.