Portfolio item number 1
Short description of portfolio item number 1
Posts by Collection
portfolio
Portfolio item number 2
Short description of portfolio item number 2
publications
On Averaging and Extrapolation for Gradient Descent
Published in ArXiv Preprint, 2024
This work considers the effect of averaging and extrapolation of the iterates of gradient descent in smooth convex optimization. We show that for several common stepsize sequences, averaging cannot improve gradient descent’s worst-case performance. In contrast, we prove a conceptually simple and computationally cheap extrapolation scheme strictly improves the worst-case convergence rate: when initialized at the origin, reporting \((1+1/\sqrt{16N\log(N)})x_N\) rather than \(x_N\) improves the best possible worst-case performance by the same amount as conducting \(O(\sqrt{N/\log(N)})\) more gradient steps.
Recommended citation: Alan Luner, Benjamin Grimmer. (2024). "On Averaging and Extrapolation for Gradient Descent." ArXiv Preprint 2402.12493.
Download Paper
Performance Estimation for Smooth and Strongly Convex Sets
Published in ArXiv Preprint, 2024
This work extends recent computer-assisted design and analysis techniques for first-order optimization over structured functions–known as performance estimation–to apply to structured sets. We prove “interpolation theorems” for smooth and strongly convex sets with Slater points and bounded diameter, showing a wide range of extremal questions amount to structured mathematical programs. Our theory provides finite-dimensional formulations of performance estimation problems for algorithms utilizing separating hyperplane oracles, linear optimization oracles, and/or projection oracles of smooth/strongly convex sets, and we demonstrate its applications.
Recommended citation: Alan Luner, Benjamin Grimmer. (2024). "Performance Estimation for Smooth and Strongly Convex Sets." ArXiv Preprint 2410.14811 .
Download Paper
talks
Talk 1 on Relevant Topic in Your Field
Published:
This is a description of your talk, which is a markdown files that can be all markdown-ified like any other post. Yay markdown!
Conference Proceeding talk 3 on Relevant Topic in Your Field
Published:
This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field.
teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
This is a description of a teaching experience. You can use markdown like any other post.
Teaching experience 2
Workshop, University 1, Department, 2015
This is a description of a teaching experience. You can use markdown like any other post.