Scalable Decentralized Algorithms for Online Personalized Mean Estimation

• URL: http://arxiv.org/abs/2402.12812v3
• Date: Wed, 8 May 2024 12:59:45 GMT
• Title: Scalable Decentralized Algorithms for Online Personalized Mean Estimation
• Authors: Franco Galante, Giovanni Neglia, Emilio Leonardi,
• Abstract summary: 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. We introduce two collaborative mean estimation algorithms: one draws inspiration from belief propagation, while the other employs a consensus-based approach.
• Score: 12.002609934938224
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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