# Quality or Quantity? Error-Informed Selective Online Learning with Gaussian Processes in Multi-Agent Systems: Extended Version

arXiv: https://arxiv.org/abs/2601.14275 · HTML: https://mlsanity.com/paper/2601.14275/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 10 Jan 2026.

## Builds on (most cited first, 14 of 14)

- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Generalized Product of Experts for Automatic and Principled Fusion of Gaussian Process Predictions](https://mlsanity.com/paper/1410.7827/) (2014)
- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [Generalized Robust Bayesian Committee Machine for Large-scale Gaussian Process Regression](https://mlsanity.com/paper/1806.00720/) (2018)
- [Hierarchical Mixture-of-Experts Model for Large-Scale Gaussian Process Regression](https://mlsanity.com/paper/1412.3078/) (2014)
- [Can Learning Deteriorate Control? Analyzing Computational Delays in Gaussian Process-Based Event-Triggered Online Learning](https://mlsanity.com/paper/2305.08169/) (2023)
- [Distributed Learning Consensus Control for Unknown Nonlinear Multi-Agent Systems based on Gaussian Processes](https://mlsanity.com/paper/2103.15929/) (2021)
- [Lightweight Distributed Gaussian Process Regression for Online Machine Learning](https://mlsanity.com/paper/2105.04738/) (2021)
- [Cooperative Online Learning for Multi-Agent System Control via Gaussian Processes with Event-Triggered Mechanism: Extended Version](https://mlsanity.com/paper/2304.05138/) (2023)
- [Cooperative Learning with Gaussian Processes for Euler-Lagrange Systems Tracking Control under Switching Topologies](https://mlsanity.com/paper/2402.03048/) (2024)
- [Streaming Generated Gaussian Process Experts for Online Learning and Control: Extended Version](https://mlsanity.com/paper/2508.03679/) (2025)
- [Resource-Efficient Cooperative Online Scalar Field Mapping via Distributed Sparse Gaussian Process Regression](https://mlsanity.com/paper/2309.10311/) (2023)
- [Whom to Trust? Elective Learning for Distributed Gaussian Process Regression](https://mlsanity.com/paper/2402.03014/) (2024)

## Built on by (most cited first, 1 of 1)

- [COIN-GP: Cooperative Online Learning in Networked Distributed Systems with Partial Measurements via Gaussian Process Regression](https://mlsanity.com/paper/2609.20598/) (2026)

## Abstract (arXiv)

Effective cooperation is pivotal in distributed learning for multi-agent systems, where the interplay between the quantity and quality of the machine learning models is crucial. This paper reveals the irrationality of indiscriminate inclusion of all models on agents for joint prediction, highlighting the imperative to prioritize quality over quantity in cooperative learning. Specifically, we present the first selective online learning framework for distributed Gaussian process (GP) regression, namely distributed error-informed GP (EIGP), that enables each agent to assess its neighboring collaborators, using the proposed selection function to choose the higher quality GP models with less prediction errors. Moreover, algorithmic enhancements are embedded within the EIGP, including a greedy algorithm (gEIGP) for accelerating prediction and an adaptive algorithm (aEIGP) for improving prediction accuracy. In addition, approaches for fast prediction and model update are introduced in conjunction with the error-informed quantification term iteration and a data deletion strategy to achieve real-time learning operations. Numerical simulations are performed to demonstrate the effectiveness of the developed methodology, showcasing its superiority over the state-of-the-art distributed GP methods with different benchmarks.