# Decentralized Online Learning for Random Inverse Problems Over Graphs

arXiv: https://arxiv.org/abs/2303.11789 · HTML: https://mlsanity.com/paper/2303.11789/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 60 references that are in the map.
- First posted on arXiv 20 Mar 2023.

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

- [Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithms](https://mlsanity.com/paper/1801.07226/) (2018)
- [On the Optimality of Averaging in Distributed Statistical Learning](https://mlsanity.com/paper/1407.2724/) (2014)
- [Online Distributed Learning Over Networks in RKH Spaces Using Random Fourier Features](https://mlsanity.com/paper/1703.08131/) (2017)
- [Formalization of a Stochastic Approximation Theorem](https://mlsanity.com/paper/2202.05959/) (2022)
- [Convergence of Unregularized Online Learning Algorithms](https://mlsanity.com/paper/1708.02939/) (2017)
- [QC-ODKLA: Quantized and Communication-Censored Online Decentralized Kernel Learning via Linearized ADMM](https://mlsanity.com/paper/2208.02777/) (2022)
- [DOT and DOP: Linearly Convergent Algorithms for Finding Fixed Points of Multi-Agent Operators](https://mlsanity.com/paper/2008.06636/) (2020)
- [Detectability, Observability and Lyapunov-Type Theorems of Linear Discrete Time-Varying Stochastic Systems with Multiplicative Noise](https://mlsanity.com/paper/1509.04379/) (2015)
- [Decentralized Online Regularized Learning Over Random Time-Varying Graphs](https://mlsanity.com/paper/2206.03861/) (2022)

## Abstract (arXiv)

We propose a decentralized online learning algorithm for distributed random inverse problems over network graphs with online measurements, and unifies the distributed parameter estimation in Hilbert spaces and the least mean square problem in reproducing kernel Hilbert spaces (RKHS-LMS). We transform the convergence of the algorithm into the asymptotic stability of a class of inhomogeneous random difference equations in Hilbert spaces with L2-bounded martingale difference terms and develop the L2-asymptotic stability theory in Hilbert spaces. We show that if the network graph is connected and the sequence of forward operators satisfies the infinite-dimensional spatio-temporal persistence of excitation condition, then the estimates of all nodes are mean square and almost surely strongly consistent. Moreover, we propose a decentralized online learning algorithm in RKHS based on non-stationary online data streams, and prove that the algorithm is mean square and almost surely strongly consistent if the operators induced by the random input data satisfy the infinite-dimensional spatio-temporal persistence of excitation condition.