报告题目：Adaptive Sampling Strategies for Stochastic Composite Optimization

报告人：陈彩华教授 南京大学

报告时间：2024年5月18日（星期六），上午10:00—11:00

报告地点：兴庆校区数学楼2-3会议室

报告摘要：This paper addresses stochastic composite problems with objective functions that consist of both smooth and nonsmooth components. In scenarios where only a gradient estimate for the smooth component is available, we propose adaptively sampling strategies for proximal gradient methods and their accelerated counterparts. The sample size used to estimate gradients in each iteration is determined based on the observed algorithm trajectory. Our algorithms are shown to achieve lower bounds in terms of total sample size and iteration steps, indicating their efficiency in both sampling and optimization. Additionally, our analysis reveals the disparity in sample sizes between adaptive and deterministic sampling strategies, highlighting the effectiveness of adaptive sampling. Furthermore, under mild conditions, we establish the asymptotic behavior of the iteration sequences. Specifically, for strongly convex objectives, the iteration sequences generated by our proposed algorithms exhibit linear convergence in distribution. Leveraging Central Limit Theorem results, we construct confidence regions for optimal solutions. Numerical experiments are conducted to empirically validate our theoretical findings.

个人简介：陈彩华，国家优秀青年基金获得者、国家自然科学基金重大项目课题负责人，现任南京大学教授、博士生导师、工程管理学院副院长。南京大学理学博士，新加坡国立大学联合培养博士。从事优化算法设计与应用、数据驱动的决策等研究，代表作发表于Mathematical Programming, SIAM系列杂志,NeurIPS, CVPR等国际知名学术期刊和会议。获华人数学家联盟最佳论文奖(2017、2018)，中国运筹学会青年科技奖(2018)，江苏省工业与应用数学学会青年奖(2020),南京大学青年五四奖章(2019)，南京大学青年五四奖章集体（2024，集体负责人）。