# Decentralized Online Regularized Learning Over Random Time-Varying Graphs

arXiv: https://arxiv.org/abs/2206.03861 · HTML: https://mlsanity.com/paper/2206.03861/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 58 references that are in the map.
- First posted on arXiv 7 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [An Online Plug-and-Play Algorithm for Regularized Image Reconstruction](https://mlsanity.com/paper/1809.04693/) (2018)
- [Optimal Algorithms for Non-Smooth Distributed Optimization in Networks](https://mlsanity.com/paper/1806.00291/) (2018)
- [Uniform regret bounds over Rd for the sequential linear regression problem with the square loss](https://mlsanity.com/paper/1805.11386/) (2018)
- [Distributed Online Linear Regression](https://mlsanity.com/paper/1902.04774/) (2019)
- [Online Learning over Dynamic Graphs via Distributed Proximal Gradient Algorithm](https://mlsanity.com/paper/1905.07018/) (2019)
- [Distributed Constrained Recursive Nonlinear Least-Squares Estimation: Algorithms and Asymptotics](https://mlsanity.com/paper/1602.00382/) (2016)
- [Resilient Distributed Estimation: Sensor Attacks](https://mlsanity.com/paper/1709.06156/) (2017)
- [Distributed Averaging With Random Network Graphs and Noises](https://mlsanity.com/paper/1702.03478/) (2017)

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

- [Decentralized Online Learning for Random Inverse Problems Over Graphs](https://mlsanity.com/paper/2303.11789/) (2023)

## Abstract (arXiv)

We study the decentralized online regularized linear regression algorithm over random time-varying graphs. At each time step, every node runs an online estimation algorithm consisting of an innovation term processing its own new measurement, a consensus term taking a weighted sum of estimations of its own and its neighbors with additive and multiplicative communication noises and a regularization term preventing over-fitting. It is not required that the regression matrices and graphs satisfy special statistical assumptions such as mutual independence, spatio-temporal independence or stationarity. We develop the nonnegative supermartingale inequality of the estimation error, and prove that the estimations of all nodes converge to the unknown true parameter vector almost surely if the algorithm gains, graphs and regression matrices jointly satisfy the sample path spatio-temporal persistence of excitation condition. Especially, this condition holds by choosing appropriate algorithm gains if the graphs are uniformly conditionally jointly connected and conditionally balanced, and the regression models of all nodes are uniformly conditionally spatio-temporally jointly observable, under which the algorithm converges in mean square and almost surely. In addition, we prove that the regret upper bound is O(T1-τln T), where τ∈ (0.5,1) is a constant depending on the algorithm gains.