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Asynchronous Distributed Gaussian Process Regression for Online Learning and Dynamical Systems: Complementary Document

Zewen Yang, Xiaobing Dai, Sandra Hirche

TL;DR

This work tackles the challenge of asynchronous distributed Gaussian Process regression for online learning in dynamical systems. It develops a local-approximation and agent-based framework to enable distributed predictions under communication delays, supported by theoretical guarantees on prediction and control performance. The paper derives delayed-prediction bounds, aggregation-based error bounds, and an ultimate tracking-error limit for control, complemented by Lipschitz analyses of common kernels. Empirical results on regression and control tasks illustrate robustness to delays and communication constraints, highlighting practical viability for online, multi-agent GP deployments.

Abstract

This is a complementary document for the paper titled "Asynchronous Distributed Gaussian Process Regression for Online Learning and Dynamical Systems".

Asynchronous Distributed Gaussian Process Regression for Online Learning and Dynamical Systems: Complementary Document

TL;DR

This work tackles the challenge of asynchronous distributed Gaussian Process regression for online learning in dynamical systems. It develops a local-approximation and agent-based framework to enable distributed predictions under communication delays, supported by theoretical guarantees on prediction and control performance. The paper derives delayed-prediction bounds, aggregation-based error bounds, and an ultimate tracking-error limit for control, complemented by Lipschitz analyses of common kernels. Empirical results on regression and control tasks illustrate robustness to delays and communication constraints, highlighting practical viability for online, multi-agent GP deployments.

Abstract

This is a complementary document for the paper titled "Asynchronous Distributed Gaussian Process Regression for Online Learning and Dynamical Systems".

Paper Structure

This paper contains 19 sections, 4 theorems, 51 equations, 6 figures, 2 tables.

Table of Contents

  1. Extended Introduction and Related Work
  2. Local Approximation Gaussian Process
  3. Agent-based Gaussian Process
  4. Proofs for Prediction Performance
  5. Proof of Lemma 3
  6. Proof of Theorem 7
  7. Proof of Corollary 8
  8. Proof for Control Performance in Theorem 9
  9. Lipschitz Continuity of Kernels
  10. Proof of Lemma 4 for SE Kernel
  11. Corollaries of the Other Lipschitz constant of Kernel
  12. Lipschitz Continuity for ARD-SE Kernel
  13. Lipschitz Continuity for Linear Kernel
  14. Lipschitz Continuity for RQ Kernel
  15. Lipschitz Continuity for Periodic Kernel
  16. ...and 4 more sections

Key Result

Corollary 1

Consider the ARD-SE kernel used and its distance function defined as then the corresponding Lipschitz constant is $L_{\kappa, \text{ARD-SE}} = \sigma_f^2\exp(-0.5)$.

Figures (6)

  • Figure 1: The delay time of the results of GP models.
  • Figure 2: The sorted delay time of the results in the information set of AsyncDGP.
  • Figure 3: The delay time of the results on SARCOS.
  • Figure 4: The delay time of the results on PUMADYN32NM.
  • Figure 5: The prediction errors and tracking errors over 1000 iterations.
  • ...and 1 more figures

Theorems & Definitions (8)

  • Corollary 1
  • proof
  • Corollary 2
  • proof
  • Corollary 3
  • proof
  • Corollary 4
  • proof