Scalable Decentralized Algorithms for Online Personalized Mean Estimation - Inria - Institut national de recherche en sciences et technologies du numérique
Pré-Publication, Document De Travail Année : 2024

Scalable Decentralized Algorithms for Online Personalized Mean Estimation

Résumé

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.

Dates et versions

hal-04762852 , version 1 (31-10-2024)

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Franco Galante, Giovanni Neglia, Emilio Leonardi. Scalable Decentralized Algorithms for Online Personalized Mean Estimation. 2024. ⟨hal-04762852⟩
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