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

In this paper, we revisit $\mathsf{\text{ROOT-SGD}}$, 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 $\mathsf{\text{ROOT-SGD}}$ 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 $\mathsf{\text{ROOT-SGD}}$ with diminishing achieves optimal convergence rates while maintaining computational efficiency. By dynamically adjusting the learning rate, $\mathsf{\text{ROOT-SGD}}$ 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.