A Universal Transfer Theorem for Convex Optimization Algorithms Using Inexact First-order Oracles
Phillip Kerger, Marco Molinaro, Hongyi Jiang, Amitabh Basu
Abstract
Given *any* algorithm for convex optimization that uses exact first-order information (i.e., function values and subgradients), we show how to use such an algorithm to solve the problem with access to *inexact* first-order information. This is done in a ``black-box'' manner without knowledge of the internal workings of the algorithm. This complements previous work that considers the performance of specific algorithms like (accelerated) gradient descent with inexact information. In particular, our results apply to a wider range of algorithms beyond variants of gradient descent, e.g., projection-free methods, cutting-plane methods, or any other first-order methods formulated in the future. Further, they also apply to algorithms that handle structured nonconvexities like mixed-integer decision variables.
BibTeX
@inproceedings{
kerger2024a,
title={A Universal Transfer Theorem for Convex Optimization Algorithms Using Inexact First-order Oracles},
author={Phillip Kerger and Marco Molinaro and Hongyi Jiang and Amitabh Basu},
booktitle={Forty-first International Conference on Machine Learning},
year={2024},
url={https://openreview.net/forum?id=aPhwhueqjR}
}