报告题目：Stochastic Approximation: AStatistical Perspective

报告时间：2022-03-23，15:10-16:10

报告地点：腾讯会议（ID：723 1564 5542）

组织单位：北京大学数学科学学院

报告人：Jiadong Liang (PKU)        

报告摘要：

Stochastic recursive algorithms,also known as stochastic approximation (SA), take many forms and have numerousapplications. Starting with the seminal work of Robbins and Monro, thesemethods are standard iterative procedures for using data to approximately solvethe root-finding problems or optimization problems. Upon obtaining somestochastic data information, the SA adopts an incremental update and theaveraged or final iterate is returned. One superiority of the SA is that itsustains only mild computational and storage costs per update. Given theseattractive computational properties, it is natural to ask if SA methods alsoachieve optimal statistical performance.

In this talk, we will conduct adetailed review of the literature on the asymptotic behavior of SA methods. Wewill see that some of them may actually reach the asymptotic efficiency boundwhose definition is analogous to that in asymptotic statistics. We will alsosee a wide range of statistical results obtained under different assumptions ofthe data generating process.