# Adaptation and learning over networks under subspace constraints -- Part II: Performance Analysis

arXiv: https://arxiv.org/abs/1906.12250 · HTML: https://mlsanity.com/paper/1906.12250/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2019.

## Built on by (most cited first, 5 of 5)

- [Quantization for decentralized learning under subspace constraints](https://mlsanity.com/paper/2209.07821/) (2022)
- [Differential error feedback for communication-efficient decentralized learning](https://mlsanity.com/paper/2406.18418/) (2024)
- [Dencentralized learning in the presence of low-rank noise](https://mlsanity.com/paper/2203.09810/) (2022)
- [Exact Subspace Diffusion for Decentralized Multitask Learning](https://mlsanity.com/paper/2304.07358/) (2023)
- [Decentralized Multitask Learning over Learned Task Graphs](https://mlsanity.com/paper/2608.26989/) (2026)

## Abstract (arXiv)

Part I of this paper considered optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in low-dimensional subspaces. Starting from the centralized projected gradient descent, an iterative and distributed solution was proposed that responds to streaming data and employs stochastic approximations in place of actual gradient vectors, which are generally unavailable. We examined the second-order stability of the learning algorithm and we showed that, for small step-sizes μ, the proposed strategy leads to small estimation errors on the order of μ. This Part II examines steady-state performance. The results reveal explicitly the influence of the gradient noise, data characteristics, and subspace constraints, on the network performance. The results also show that in the small step-size regime, the iterates generated by the distributed algorithm achieve the centralized steady-state performance.