Collaborative Algorithms for Online Personalized Mean Estimation

TL;DR

This paper introduces a collaborative algorithm for online personalized mean estimation where agents communicate to improve their estimates, even when the number of agents with the same mean is unknown, with proven efficiency and extensions to clustering scenarios.

Contribution

The paper proposes a novel collaborative strategy for online mean estimation that handles unknown cluster sizes and extends to cluster-based estimation.

Findings

Algorithm improves mean estimates through communication.

Variants demonstrate strong numerical performance.

Extension to cluster-based mean estimation.

Abstract

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.