| PhD Viva

Name of the Speaker: Mr. Anik Kumar Paul (EE18D030)
Guide: Prof. Arunkumar D Mahindrakar
Co-Guide: Dr. Rachel Kalpana Kalaimani
Online meeting link: https://meet.google.com/iur-znsq-mgh
Date/Time: 3rd December 2024 (Tuesday), 10:00 AM
Title: Analysis of Stochastic Mirror Descent Algorithms: Bridging Continuous and Discrete Domains

Abstract :

The mirror descent algorithm, originally conceived as a generalization of the gradient descent algorithm into non-Euclidean space, establishes a sophisticated framework that yields a profound geometric interpretation for optimizing problems across various domains. This work focuses on two key aspects. First, it establishes the equivalence between the mirror descent algorithm and a projected dynamical system in a non-Euclidean domain, a nuanced generalization compared to continuous-time gradient flow. This connection highlights the geometric foundation of the algorithm and its versatility in handling constrained optimization problems. The second aspect examines the almost sure convergence of different variants of zeroth-order stochastic mirror descent algorithm. By leveraging both the dynamical systems viewpoint and martingale theory, the almost sure convergence of the iterates is rigorously shown. Additionally, a finite-time analysis is provided that derives concentration inequalities that characterize the behavior of the iterates at specific finite times. These findings offer a deeper understanding of the performance and reliability of zeroth-order stochastic mirror descent algorithms under more flexible assumptions.