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.

翻译：本文重新审视了\textsf{ROOT-SGD}——一种旨在弥合随机优化与统计效率之间差距的创新随机优化方法。所提出的方法通过整合精心设计的\emph{递减步长策略}，提升了\textsf{ROOT-SGD}的性能与可靠性。该策略解决了优化中的关键挑战，提供了坚实的理论保证与实践优势。我们的分析表明，采用递减步长的\textsf{ROOT-SGD}在保持计算效率的同时实现了最优收敛速率。通过动态调整学习率，\textsf{ROOT-SGD}确保了整个优化过程中稳定性和精度的提升。本研究结果为开发兼具高效性与统计鲁棒性的先进优化算法提供了重要洞见。