# Nonlinear Perturbation-based Non-Convex Optimization over Time-Varying Networks

arXiv: https://arxiv.org/abs/2408.02269 · HTML: https://mlsanity.com/paper/2408.02269/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2024.

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

- [Communication-Efficient Personalized Distributed Learning with Data and Node Heterogeneity](https://mlsanity.com/paper/2504.17520/) (2025)

## Abstract (arXiv)

Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a computationally efficient algorithm that solves distributed convex problems and optimally finds the solution to locally non-convex objective functions. In contrast to batch gradient optimization in some literature, our algorithm is on a single-time scale with no extra inner consensus loop. It evaluates one gradient entry per node per time. Further, the algorithm addresses link-level nonlinearity representing, for example, logarithmic quantization of the exchanged data or clipping of the exchanged data bits. Leveraging perturbation-based theory and algebraic Laplacian network analysis proves optimal convergence and dynamics stability over time-varying and switching networks. The time-varying network setup might be due to packet drops or link failures. Despite the nonlinear nature of the dynamics, we prove exact convergence in the face of odd sign-preserving sector-bound nonlinear data transmission over the links. Illustrative numerical simulations further highlight our contributions.