随机镜像后裔算法的几乎确定收敛性和非渐近集中限界

IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS IEEE Control Systems Letters Pub Date : 2024-10-16 DOI:10.1109/LCSYS.2024.3482148

Anik Kumar Paul;Arun D. Mahindrakar;Rachel K. Kalaimani

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引用次数: 0

摘要

这篇文章研究了利用偏置随机子梯度的随机镜像后裔（SMD）算法的收敛性和集中特性。在偏差递减的假设下，我们确定了算法迭代的几乎确定收敛性。此外，我们还基于标准假设，推导出了迭代函数值与最优值之间差异的集中约束。随后，利用随机子梯度中的亚高斯噪声假设，我们提出了这一差异的精炼集中限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Almost Sure Convergence and Non-Asymptotic Concentration Bounds for Stochastic Mirror Descent Algorithm

This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm’s iterates under the assumption of diminishing bias. Furthermore, we derive concentration bounds for the discrepancy between the iterates’ function values and the optimal value, based on standard assumptions. Subsequently, leveraging the assumption of Sub-Gaussian noise in stochastic subgradients, we present refined concentration bounds for this discrepancy.

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来源期刊

IEEE Control Systems Letters Mathematics-Control and Optimization

CiteScore

4.40

自引率

13.30%

发文量

471