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Streaming Generated Gaussian Process Experts for Online Learning and Control: Extended Version

Zewen Yang, Dongfa Zhang, Xiaobing Dai, Fengyi Yu, Chi Zhang, Bingkun Huang, Hamid Sadeghian, Sami Haddadin

TL;DR

SkyGP tackles online learning for safety-critical dynamics by replacing exact Gaussian Process inference with a bounded, streaming ensemble of GP experts whose allocation is guided by kernel-induced centers. The approach introduces a progressive expert generation strategy, time-aware data weighting, and MoE/PoE/BCM-style aggregation to maintain accuracy with bounded computation and memory. A probabilistic error bound is derived for the aggregated predictor, which underpins a safe learning-based control policy applied to general nonlinear systems and Euler-Lagrange dynamics, with theoretical guarantees on tracking performance. Empirically, SkyGP achieves strong regression accuracy and real-time control performance across multiple benchmarks, outperforming state-of-the-art scalable GP methods while offering flexible trade-offs between latency and accuracy. The method holds promise for deploying uncertainty-aware learning in real-time robotic and autonomous systems, with noted limitations in center updates and rapid distribution shifts.

Abstract

Gaussian Processes (GPs), as a nonparametric learning method, offer flexible modeling capabilities and calibrated uncertainty quantification for function approximations. Additionally, GPs support online learning by efficiently incorporating new data with polynomial-time computation, making them well-suited for safety-critical dynamical systems that require rapid adaptation. However, the inference and online updates of exact GPs, when processing streaming data, incur cubic computation time and quadratic storage memory complexity, limiting their scalability to large datasets in real-time settings. In this paper, we propose a streaming kernel-induced progressively generated expert framework of Gaussian processes (SkyGP) that addresses both computational and memory constraints by maintaining a bounded set of experts, while inheriting the learning performance guarantees from exact Gaussian processes. Furthermore, two SkyGP variants are introduced, each tailored to a specific objective, either maximizing prediction accuracy (SkyGP-Dense) or improving computational efficiency (SkyGP-Fast). The effectiveness of SkyGP is validated through extensive benchmarks and real-time control experiments demonstrating its superior performance compared to state-of-the-art approaches.

Streaming Generated Gaussian Process Experts for Online Learning and Control: Extended Version

TL;DR

SkyGP tackles online learning for safety-critical dynamics by replacing exact Gaussian Process inference with a bounded, streaming ensemble of GP experts whose allocation is guided by kernel-induced centers. The approach introduces a progressive expert generation strategy, time-aware data weighting, and MoE/PoE/BCM-style aggregation to maintain accuracy with bounded computation and memory. A probabilistic error bound is derived for the aggregated predictor, which underpins a safe learning-based control policy applied to general nonlinear systems and Euler-Lagrange dynamics, with theoretical guarantees on tracking performance. Empirically, SkyGP achieves strong regression accuracy and real-time control performance across multiple benchmarks, outperforming state-of-the-art scalable GP methods while offering flexible trade-offs between latency and accuracy. The method holds promise for deploying uncertainty-aware learning in real-time robotic and autonomous systems, with noted limitations in center updates and rapid distribution shifts.

Abstract

Gaussian Processes (GPs), as a nonparametric learning method, offer flexible modeling capabilities and calibrated uncertainty quantification for function approximations. Additionally, GPs support online learning by efficiently incorporating new data with polynomial-time computation, making them well-suited for safety-critical dynamical systems that require rapid adaptation. However, the inference and online updates of exact GPs, when processing streaming data, incur cubic computation time and quadratic storage memory complexity, limiting their scalability to large datasets in real-time settings. In this paper, we propose a streaming kernel-induced progressively generated expert framework of Gaussian processes (SkyGP) that addresses both computational and memory constraints by maintaining a bounded set of experts, while inheriting the learning performance guarantees from exact Gaussian processes. Furthermore, two SkyGP variants are introduced, each tailored to a specific objective, either maximizing prediction accuracy (SkyGP-Dense) or improving computational efficiency (SkyGP-Fast). The effectiveness of SkyGP is validated through extensive benchmarks and real-time control experiments demonstrating its superior performance compared to state-of-the-art approaches.

Paper Structure

This paper contains 29 sections, 3 theorems, 41 equations, 12 figures, 11 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement and Preliminaries
  3. Generated Experts of Gaussian Processes
  4. Kernel-Induced Distance
  5. Progressive Expert Generation Strategy
  6. Expert Localization and Generation
  7. Dynamic Expert List Creation
  8. Aggregated Prediction
  9. Bounded Complexity Analysis
  10. Model Update
  11. Prediction
  12. Safe Learning-based Control Policy
  13. Learning Performance of SkyGP
  14. Safe Critical Control Application
  15. A General Control System
  16. ...and 14 more sections

Key Result

Lemma 1

Consider the regression task in a compact domain $\mathbb{X}$, and suppose the kernel function $\kappa(\cdot, \cdot)$ is Lipschitz with Lipschitz constant $L_{\kappa} \in \mathbb{R}_{0,+}$. Choose $\delta \in (0,1 / \bar{\mathcal{N}})$ and $\tau \in \mathbb{R}_+$, then the prediction error satisfies with a probability of at least $1 - \bar{\mathcal{N}} \delta$, where $\gamma(\bm{x}) = \sum\nolimit

Figures (12)

  • Figure 1:
  • Figure 2: Learning and tracking performance comparison of the control task from the $100$ times Monte Carlo tests.
  • Figure 3: SMSE comparison on SARCOS dataset against all baselines.
  • Figure 4: SMSE comparison on PUMA dataset against all baselines.
  • Figure 5: SMSE comparison on KIN40K dataset against all baselines.
  • ...and 7 more figures

Theorems & Definitions (8)

  • Remark 1
  • Lemma 1
  • Remark 2
  • Theorem 1
  • Theorem 2
  • proof
  • proof
  • proof