Stochastic Processes Seminar

Date: March 29, 2024

Time: 10:00AM - 11:00AM

Location: ZOOM

Speaker: Nhu Nguyen, University of Rhode Island

Title: Stochastic Approximation with Discontinuous Dynamics, Differential Inclusions, and Applications

Abstract: This talk develops new results for stochastic approximation algorithms. The emphasis is on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, non-smooth analysis, and stochastic differential inclusions. Under broad conditions, it is shown that a suitably scaled sequence of the iterates has a differential inclusion limit. In addition, it is shown for the first time that a centered and scaled sequence of the iterates converges weakly to a stochastic differential inclusion limit. The results are then used to treat several application examples, including the Markov decision process, Lasso algorithms, Pegasos algorithms, support vector machine classification, and learning.