# A Distributed Quasi-Newton Algorithm for Empirical Risk Minimization with Nonsmooth Regularization

arXiv: https://arxiv.org/abs/1803.01370 · HTML: https://mlsanity.com/paper/1803.01370/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2018.

## Built on by (most cited first, 4 of 4)

- [Multiple Greedy Quasi-Newton Methods for Saddle Point Problems](https://mlsanity.com/paper/2408.00241/) (2024)
- [Quasi-Newton Updating for Large-Scale Distributed Learning](https://mlsanity.com/paper/2306.04111/) (2023)
- [Quantized Adaptive Subgradient Algorithms and Their Applications](https://mlsanity.com/paper/2208.05631/) (2022)
- [A Selective Review on Statistical Methods for Massive Data Computation: Distributed Computing, Subsampling, and Minibatch Techniques](https://mlsanity.com/paper/2403.11163/) (2024)

## Abstract (arXiv)

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this problem either do not work well in the distributed setting or work only for specific regularizers. Our algorithm uses successive quadratic approximations, and we describe how to maintain an approximation of the Hessian and solve subproblems efficiently in a distributed manner. The proposed method enjoys global linear convergence for a broad range of non-strongly convex problems that includes the most commonly used ERMs, thus requiring lower communication complexity. It also converges on non-convex problems, so has the potential to be used on applications such as deep learning. Initial computational results on convex problems demonstrate that our method significantly improves on communication cost and running time over the current state-of-the-art methods.