# A Universal Transfer Theorem for Convex Optimization Algorithms Using Inexact First-order Oracles

arXiv: https://arxiv.org/abs/2406.00576 · HTML: https://mlsanity.com/paper/2406.00576/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2024.

## Built on by (most cited first, 1 of 1)

- [Distributed Learning with Adversarial Gradient Perturbations](https://mlsanity.com/paper/2605.03313/) (2026)

## Abstract (arXiv)

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.