# Collaborative Algorithms for Online Personalized Mean Estimation

arXiv: https://arxiv.org/abs/2208.11530 · HTML: https://mlsanity.com/paper/2208.11530/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 38 references that are in the map.
- First posted on arXiv 24 Aug 2022.

## Builds on (most cited first, 23 of 23)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [Personalized Federated Learning: A Meta-Learning Approach](https://mlsanity.com/paper/2002.07948/) (2020)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
- [Lower Bounds and Optimal Algorithms for Personalized Federated Learning](https://mlsanity.com/paper/2010.02372/) (2020)
- [Decentralized Collaborative Learning of Personalized Models over Networks](https://mlsanity.com/paper/1610.05202/) (2016)
- [Federated Multi-armed Bandits with Personalization](https://mlsanity.com/paper/2102.13101/) (2021)
- [Federated Multi-Armed Bandits](https://mlsanity.com/paper/2101.12204/) (2021)
- [Nearly Optimal Adaptive Procedure with Change Detection for Piecewise-Stationary Bandit](https://mlsanity.com/paper/1802.03692/) (2018)
- [Social Learning in Multi Agent Multi Armed Bandits](https://mlsanity.com/paper/1910.02100/) (2019)
- [SIC-MMAB: Synchronisation Involves Communication in Multiplayer Multi-Armed Bandits](https://mlsanity.com/paper/1809.08151/) (2018)
- [Distributed Exploration in Multi-Armed Bandits](https://mlsanity.com/paper/1311.0800/) (2013)
- [Collaborative Learning with Limited Interaction: Tight Bounds for Distributed Exploration in Multi-Armed Bandits](https://mlsanity.com/paper/1904.03293/) (2019)
- [Distributed Cooperative Decision Making in Multi-agent Multi-armed Bandits](https://mlsanity.com/paper/2003.01312/) (2020)
- [A Practical Algorithm for Multiplayer Bandits when Arm Means Vary Among Players](https://mlsanity.com/paper/1902.01239/) (2019)
- [Near-Optimal Collaborative Learning in Bandits](https://mlsanity.com/paper/2206.00121/) (2022)
- [One More Step Towards Reality: Cooperative Bandits with Imperfect Communication](https://mlsanity.com/paper/2111.12482/) (2021)
- [Best Arm Identification in Spectral Bandits](https://mlsanity.com/paper/2005.09841/) (2020)
- [Federated Asymptotics: a model to compare federated learning algorithms](https://mlsanity.com/paper/2108.07313/) (2021)
- [Machine learning and data analytics for the IoT](https://mlsanity.com/paper/2007.04093/) (2020)
- [Parallel Best Arm Identification in Heterogeneous Environments](https://mlsanity.com/paper/2207.08015/) (2022)
- [A Practical Bias Estimation Algorithm for Multisensor--Multitarget Tracking](https://mlsanity.com/paper/1603.03449/) (2016)

## Built on by (most cited first, 5 of 5)

- [Online Learning from Strategic Human Feedback in LLM Fine-Tuning](https://mlsanity.com/paper/2412.16834/) (2024)
- [Scalable Decentralized Algorithms for Online Personalized Mean Estimation](https://mlsanity.com/paper/2402.12812/) (2024)
- [Differentially-Private Collaborative Online Personalized Mean Estimation](https://mlsanity.com/paper/2411.07094/) (2024)
- [Communication-Constrained Private Decentralized Online Personalized Mean Estimation](https://mlsanity.com/paper/2511.04702/) (2025)
- [Truthful Online Preference Aggregation for LLM Fine-Tuning in Mobile Crowdsourcing](https://mlsanity.com/paper/2605.24052/) (2026)

## Abstract (arXiv)

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.