# Non-Convex Distributed Optimization

arXiv: https://arxiv.org/abs/1512.00895 · HTML: https://mlsanity.com/paper/1512.00895/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2015.

## Built on by (most cited first, 9 of 9)

- [Decentralized Stochastic Optimization with Inherent Privacy Protection](https://mlsanity.com/paper/2205.03884/) (2022)
- [Decentralized Nonconvex Optimization with Guaranteed Privacy and Accuracy](https://mlsanity.com/paper/2212.07534/) (2022)
- [Quantization enabled Privacy Protection in Decentralized Stochastic Optimization](https://mlsanity.com/paper/2208.04845/) (2022)
- [BSAC-CoEx: Coexistence of URLLC and Distributed Learning Services via Device Selection](https://mlsanity.com/paper/2212.11805/) (2022)
- [Distributed optimization: designed for federated learning](https://mlsanity.com/paper/2508.08606/) (2025)
- [Distributed Optimization via Kernelized Multi-armed Bandits](https://mlsanity.com/paper/2312.04719/) (2023)
- [An Asynchronous Decentralised Optimisation Algorithm for Nonconvex Problems](https://mlsanity.com/paper/2507.22311/) (2025)
- [Convex and Non-convex Federated Learning with Stale Stochastic Gradients: Diminishing Step Size is All You Need](https://mlsanity.com/paper/2603.02639/) (2026)
- [A Unified Framework for Fair and Personalized Decentralized Learning under Communication Constraints](https://mlsanity.com/paper/2608.26493/) (2026)

## Abstract (arXiv)

We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. We generalize the results obtained previously to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function. Our analysis shows that this noised procedure converges at a rate of O(1/t).