应用数学青年讨论班（午餐会）——Investigating Accelerated Gradient Methods with Inexact Oracles via Performance Estimation Problem
报告人：刘茵（bat365中国在线平台官方网站）
时间：2024-12-25 12:15-13:30
地点：智华楼四元厅225
摘要：
First-order algorithms are widely used in optimization due to their simplicity and scalability. However, in many applications, obtaining exact gradients is computationally expensive or impractical, sparking interest in understanding their performance under inexact oracle settings. Accelerated methods, while efficient, are particularly sensitive to gradient errors compared to their non-accelerated counterparts. In this talk, we analyze the nonasymptotic convergence bounds of two accelerated methods—Inexact Optimized Gradient Method (OGM) and Inexact Fast Gradient Method (FGM)—applied to deterministic smooth convex problems. Using the Performance Estimation Problem (PEP) framework, we derive novel bounds under the absolute error assumption, showing that accumulated errors are independent of initial conditions or algorithm trajectories. Additionally, we explore the tradeoff between convergence rate and accumulated error, providing insights into optimal stepsize selection and gradient inexactness allocation. These results have important implications for designing robust optimization algorithms in real-world, inexact settings.
报告人简介：
刘茵，bat365中国在线平台官方网站拟入站博雅博士后，博士毕业于美国俄亥俄州立大学综合系统工程系，导师 Professor Sam Davanloo Tajbakhsh。她的研究领域主要集中在一阶算法的理论分析，致力于提升优化算法在解决复杂现实问题中的高效性与适用性。
欢迎大家参与12月25号的午餐会。报告时间是12:30-13:30，午餐于12:15开始提供。
请有意参与并需要餐食的老师和同学在12月24日15:00前填写以下问卷：https://www.wjx.cn/vm/taFQKBI.aspx。
