[2510.16232] Personalized Collaborative Learning with Affinity-Based Variance Reduction

Statistics > Machine Learning arXiv:2510.16232 (stat) [Submitted on 17 Oct 2025 (v1), last revised 2 Mar 2026 (this version, v2)] Title:Personalized Collaborative Learning with Affinity-Based Variance Reduction Authors:Chenyu Zhang, Navid Azizan View a PDF of the paper titled Personalized Collaborative Learning with Affinity-Based Variance Reduction, by Chenyu Zhang and Navid Azizan View PDF Abstract:Multi-agent learning faces a fundamental tension: leveraging distributed collaboration without sacrificing the personalization needed for diverse agents. This tension intensifies when aiming for full personalization while adapting to unknown heterogeneity levels -- gaining collaborative speedup when agents are similar, without performance degradation when they are different. Embracing the challenge, we propose personalized collaborative learning (PCL), a novel framework for heterogeneous agents to collaboratively learn personalized solutions with seamless adaptivity. Through carefully designed bias correction and importance correction mechanisms, our method AffPCL robustly handles both environment and objective heterogeneity. We prove that AffPCL reduces sample complexity over independent learning by a factor of $\max\{n^{-1}, \delta\}$, where $n$ is the number of agents and $\delta\in[0,1]$ measures their heterogeneity. This affinity-based acceleration automatically interpolates between the linear speedup of federated learning in homogeneous settings and the baseline of indep...