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.
Categories: stat.ML cs.LG math.OC