# Quantized Frank-Wolfe: Faster Optimization, Lower Communication, and Projection Free

arXiv: https://arxiv.org/abs/1902.06332 · HTML: https://mlsanity.com/paper/1902.06332/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2019.

## Built on by (most cited first, 2 of 2)

- [QC-ODKLA: Quantized and Communication-Censored Online Decentralized Kernel Learning via Linearized ADMM](https://mlsanity.com/paper/2208.02777/) (2022)
- [Decentralized Entropic Optimal Transport for Distributed Distribution Comparison](https://mlsanity.com/paper/2301.12065/) (2023)

## Abstract (arXiv)

How can we efficiently mitigate the overhead of gradient communications in distributed optimization? This problem is at the heart of training scalable machine learning models and has been mainly studied in the unconstrained setting. In this paper, we propose Quantized-Frank-Wolfe (QFW), the first projection-free and communication-efficient algorithm for solving constrained optimization problems at scale. We consider both convex and non-convex objective functions, expressed as a finite-sum or more generally a stochastic optimization problem, and provide strong theoretical guarantees on the convergence rate of QFW. This is accomplished by proposing novel quantization schemes that efficiently compress gradients while controlling the noise variance introduced during this process. Finally, we empirically validate the efficiency of QFW in terms of communication and the quality of returned solution against natural baselines.