Collaborative Algorithms for Online Personalized Mean Estimation
This work addresses the challenge of efficient mean estimation in distributed systems where agents have unknown shared means, offering a solution for applications like sensor networks or collaborative learning, though it appears incremental as it builds on existing estimation and clustering methods.
The paper tackles the problem of online personalized mean estimation for agents with potentially shared distribution means, introducing a collaborative algorithm that improves individual estimates through communication, with analysis of time complexity and variants showing good performance in experiments.
We consider an online estimation problem involving a set of agents. Each agent has access to a (personal) process that generates samples from a real-valued distribution and seeks to estimate its mean. We study the case where some of the distributions have the same mean, and the agents are allowed to actively query information from other agents. The goal is to design an algorithm that enables each agent to improve its mean estimate thanks to communication with other agents. The means as well as the number of distributions with same mean are unknown, which makes the task nontrivial. We introduce a novel collaborative strategy to solve this online personalized mean estimation problem. We analyze its time complexity and introduce variants that enjoy good performance in numerical experiments. We also extend our approach to the setting where clusters of agents with similar means seek to estimate the mean of their cluster.