# Distributed Online Linear Regression

arXiv: https://arxiv.org/abs/1902.04774 · HTML: https://mlsanity.com/paper/1902.04774/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2019.

## Built on by (most cited first, 10 of 10)

- [Dynamic Regret Analysis of Safe Distributed Online Optimization for Convex and Non-convex Problems](https://mlsanity.com/paper/2302.12320/) (2023)
- [Distributed Online Optimization with Stochastic Agent Availability](https://mlsanity.com/paper/2411.16477/) (2024)
- [Lazy Queries Can Reduce Variance in Zeroth-order Optimization](https://mlsanity.com/paper/2206.07126/) (2022)
- [Distributed Gradient Descent for Functional Learning](https://mlsanity.com/paper/2305.07408/) (2023)
- [Decentralized Online Convex Optimization with Unknown Feedback Delays](https://mlsanity.com/paper/2601.07901/) (2026)
- [A Survey on Distributed Online Optimization and Game](https://mlsanity.com/paper/2205.00473/) (2022)
- [Decentralized Online Regularized Learning Over Random Time-Varying Graphs](https://mlsanity.com/paper/2206.03861/) (2022)
- [Continual Learning with Distributed Optimization: Does CoCoA Forget?](https://mlsanity.com/paper/2211.16994/) (2022)
- [No-regret learning for repeated non-cooperative games with lossy bandits](https://mlsanity.com/paper/2205.06968/) (2022)
- [Finite Sample Guarantees for Distributed Online Parameter Estimation with Communication Costs](https://mlsanity.com/paper/2209.06678/) (2022)

## Abstract (arXiv)

We study online linear regression problems in a distributed setting, where the data is spread over a network. In each round, each network node proposes a linear predictor, with the objective of fitting the network-wide data. It then updates its predictor for the next round according to the received local feedback and information received from neighboring nodes. The predictions made at a given node are assessed through the notion of regret, defined as the difference between their cumulative network-wide square errors and those of the best off-line network-wide linear predictor. Various scenarios are investigated, depending on the nature of the local feedback (full information or bandit feedback), on the set of available predictors (the decision set), and the way data is generated (by an oblivious or adaptive adversary). We propose simple and natural distributed regression algorithms, involving, at each node and in each round, a local gradient descent step and a communication and averaging step where nodes aim at aligning their predictors to those of their neighbors. We establish regret upper bounds typically in cal O(T3/4) when the decision set is unbounded and in cal O(√T) in case of bounded decision set.