Overview of My Research
My current research focuses on designing, characterizing, and classifying optimal methods for convex minimization. Given an algorithm (e.g. gradient descent), one may analyze the worst-case performance among a set of problem instances (e.g. convex functions with Lipschitz gradient). Classical results give proofs of convergence guarantees. Performance estimation optimizes these proofs. Algorithm design optimizes these methods.
A recent and related interest of mine has aligned with interpolation theory: what conditions are needed for a set of observations (points, function values, gradients, etc.) to be the data of a function in some structured class? Answering these questions often yields a tractable way to analyze the performance of a given algorithm, while providing insight into the geometry of the aforementioned structure. Regardless, they make for fun interactive graphs.
Previously, I have worked on designing methods for function possessing varying levels of smoothness, interpolating the smoothness between Lipschitz functions and those with Lipschitz gradient. My first paper focused on heterogeneous compositions of such functions; each component could vary in its smoothness. Dually, each component could range in its convexity (ranging from standard convexity to strong convexity). Our main contirubutions provide universal algorithms which only take as function parameters two constants $L_{\varepsilon,r}^\mathtt{ADA}$ and $\mu_{\varepsilon}^\mathtt{ADA}$, agreggating all the upper and lower bounding curvature.
Published Papers
(IMA Journal of Numerical Analysis) arXiv
Preprints
Slides
Feel free to use my chalk studio to generate custom text, math, or images for your presentations.
