报告题目：Gradient Tracking Methods for Distributed StochasticOptimization Problems with Decision-dependent Distributions
报告人：刘永朝
报告人简介：刘永朝，大连理工大学数学科学bet365手机网址教授、博士生导师。2005年和2008年于大连海事大学数学系获得学士和硕士学位，2011年于大连理工大学数学科学bet365手机网址获得博士学位，2014年11月至2016年4月在南安普顿大学从事博士后研究。刘永朝主要研究方向为随机最优化，发表学术论文三十余篇，部分论文发表于Mathematical Programming，SIAM Journal on Optimization，Mathematics of Operations Research，SIAM Journal on Numerical Analysis期刊。
报告内容简介：This paper aims to seek the performative stable solution and the optimal solution of the distributed stochastic optimization problem with decision-dependent distributions, which is a finite-sum stochastic optimization problem over a network and the distribution depends on the decision variables. For the performative stable solution, we provide an algorithm, DSGTD-GD, which combines the distributed stochastic gradient tracking descent method with the greedy deployment scheme. Under the constant step size policy, we show that the iterates generated by DSGTD-GD converge linearly, in expectation, to a neighborhood of the performative stable solution. Under the diminishing step size policy, we show that the iterates generated by DSGTD-GD converge to the performative stable solution with rate $\mathcal{O}\left(\frac{1}{k}\right)$. Moreover, we establish that the deviation between the averaged iterates of DSGTD-GD and the performative stable solution converges in distribution to a normal random vector. For the optimal solution, we provide an algorithm, DSGTD-AG, which combines the distributed stochastic gradient tracking descent method with the adaptive gradient scheme. Under the constant step size policy, we show that the iterates generated by DSGTD-AG converge to a stationary solution with rate of $\mathcal{O}(\frac{\ln K}{\sqrt{K}})$, where $K$ is the number of iterations. The effectiveness of DSGTD-GD and DSGTD-AG is further demonstrated numerically with synthetic and real-world data.
报告时间：2025年11月30日11:15
报告地点：实训楼109
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