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

Zewen Yang, Xiaobing Dai, Jiajun Cheng, Yulong Huang, Peng Shi

TL;DR

This paper presents 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.

Abstract

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.

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

TL;DR

This paper presents 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.

Abstract

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.
Paper Structure (24 sections, 3 theorems, 45 equations, 10 figures, 1 table, 2 algorithms)

This paper contains 24 sections, 3 theorems, 45 equations, 10 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Notation and Graph Theory
  4. Notation
  5. Graph Theory
  6. Objective
  7. Gaussian Process Regression
  8. Training Dataset
  9. Online Learning with GPs
  10. Error-Informed Cooperative Learning
  11. Error-Informed Prediction Quantification
  12. Model Update Strategy
  13. Error-informed Gaussian Process Regression
  14. Greedy EIGP
  15. Adaptive EIGP
  16. ...and 9 more sections

Key Result

Lemma 1

Consider a GP model with data set $\mathbb{D}_i(t_k)$ available at $t_k$ satisfying ass_dataset and ass_GP. Choose $\tau \in \mathbb{R}_+$, $\delta \in (0,1)$ and $\delta_n \in (0,1)$ such that $\delta_{\rho} = 1 - n + n(1 - \delta)^d - \delta_n$ belongs to $(0,1)$, then $\varepsilon_i(\boldsymbol{x with probability of at least $1 - \delta_{\rho}$.

Figures (10)

  • Figure 1: Training data sets, true function, and agent quantity. Training data sets and true value of the function (above). The overall quantity of the agents included within the MAS for each iteration (below).
  • Figure 2: Predictions of different methods (above) and the absolute errors between predictions and true values. (bottom).
  • Figure 3: Prediction time for each iteration.
  • Figure 4: The plots of SMSE of each iteration with KIN40K (above) and POL (bottom) data sets.
  • Figure 5: The plots of SMSE of each iteration with KIN40K data sets in the 8-agent MAS.
  • ...and 5 more figures

Theorems & Definitions (10)

  • Remark 1
  • Remark 2
  • Lemma 1
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Lemma 2
  • Remark 7
  • Theorem 1