Abstract: Stochastic recursive algorithms, also known as stochastic approximation (SA), take many forms and have numerous applications. Starting with the seminal work of Robbins and Monro, these methods are standard iterative procedures for using data to approximately solve the root-finding problems or optimization problems. Upon obtaining some stochastic data information, the SA adopts an incremental update and the averaged or final iterate is returned. One superiority of the SA is that it sustains only mild computational and storage costs per update. Given these attractive computational properties, it is natural to ask if SA methods also achieve optimal statistical performance.

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