# Smoothed Normalization for Efficient Distributed Private Optimization

Source: [Smoothed Normalization for Efficient Distributed Private Optimization](<https://www.sota2.com/research/paper/68fa5cff1e209131ce9d608e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:59:20.361Z

Authors: Egor Shulgin, Sarit Khirirat, Peter Richt\\'arik

Published: 2025-02-19T07:10:32.000Z

## Abstract

Federated learning enables training machine learning models while preserving the privacy of participants. Surprisingly, there is no differentially private distributed method for smooth, non-convex optimization problems. The reason is that standard privacy techniques require bounding the participants' contributions, usually enforced via $\\textit{clipping}$ of the updates. Existing literature typically ignores the effect of clipping by assuming the boundedness of gradient norms or analyzes distributed algorithms with clipping but ignores DP constraints. In this work, we study an alternative approach via $\\textit{smoothed normalization}$ of the updates motivated by its favorable performance in the single-node setting. By integrating smoothed normalization with an error-feedback mechanism, we design a new distributed algorithm $\\alpha$-$\\sf NormEC$. We prove that our method achieves a superior convergence rate over prior works. By extending $\\alpha$-$\\sf NormEC$ to the DP setting, we obtain the first differentially private distributed optimization algorithm with provable convergence guarantees. Finally, our empirical results from neural network training indicate robust convergence of $\\alpha$-$\\sf NormEC$ across different parameter settings.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Classification on MNIST (test) (Epsilon-based Robustness Evaluation)](<https://www.sota2.com/research/sota/image-classification-on-mnist-test-epsilon-based-robustness-evaluation.md>): Image Classification; MNIST (test); Accuracy (epsilon=3): 10.4.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2502.13482>)

[PDF](<https://arxiv.org/pdf/2502.13482.pdf>)