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

• URL: http://arxiv.org/abs/2407.10955v2
• Date: Tue, 16 Jul 2024 09:59:35 GMT
• Title: Enhancing Stochastic Optimization for Statistical Efficiency Using ROOT-SGD with Diminishing Stepsize
• Authors: Tong Zhang, Chris Junchi Li,
• Abstract summary: This paper revisits textsfROOT-SGD, an innovative method for optimization to bridge the gap between optimization and statistical efficiency. The proposed method enhances the performance and reliability of textsfROOT-SGD by integrating a carefully designed emphdiminishing stepsize strategy.
• Score: 13.365997574848759
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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