In optimization and machine learning, a core task is to find quickly converging methods for optimizing various functions (such as loss functions). For a class of functions known as smooth strongly convex functions, gradient descent methods have been shown to have good performance and linear convergence rates. However, strong convexity is a strong condition for functions to satisfy, so we consider a relaxation of the strong convexity condition known as the Polyak-Lojasiewicz (PL) condition. The goal of this project is to develop a deeper understanding of functions satisfying the PL condition through analysis of methods such as accelerated gradient descent and proximal point methods.

The effectiveness of classical optimization methods in machine learning fascinates me, and I have always wanted to pursue research on the deeper theoretical and technical pearls underlying them. This project provides a unique opportunity for me to combine various skills in mathematics, machine learning, and statistics and will help me gain insight into the process researchers take when developing and analyzing new optimization strategies.