Scalable Decentralized Algorithms for Online Personalized Mean Estimation
Abstract
In numerous settings, agents lack sufficient data to directly learn a model. Collaborating with other agents may help, but it introduces a bias-variance trade-off, when local data distributions differ. A key challenge is for each agent to identify clients with similar distributions while learning the model, a problem that remains largely unresolved. This study focuses on a simplified version of the overarching problem, where each agent collects samples from a real-valued distribution over time to estimate its mean. Existing algorithms face impractical space and time complexities (quadratic in the number of agents A). To address scalability challenges, we propose a framework where agents self-organize into a graph, allowing each agent to communicate with only a selected number of peers r. We introduce two collaborative mean estimation algorithms: one draws inspiration from belief propagation, while the other employs a consensus-based approach, with complexity of O( r |A| log |A|) and O(r |A|), respectively. We establish conditions under which both algorithms yield asymptotically optimal estimates and offer a theoretical characterization of their performance.
Cite
@article{arxiv.2402.12812,
title = {Scalable Decentralized Algorithms for Online Personalized Mean Estimation},
author = {Franco Galante and Giovanni Neglia and Emilio Leonardi},
journal= {arXiv preprint arXiv:2402.12812},
year = {2025}
}