Federated Gaussian Process Learning via Pseudo-Representations for Large-Scale Multi-Robot Systems

TL;DR

The paper addresses scalable, privacy-preserving Gaussian Process learning for large-scale, federated multi-robot systems. It introduces pxpGP, which constructs local pseudo-datasets via sparse variational inference and augments them with boundary and repulsive penalties to yield informative, well-spread representations, shared among agents. A scaled proximal-inexact consensus ADMM (pxADMM) framework enables both centralized (pxpGP) and decentralized (dec-pxpGP) training with warm-starts and adaptive parameter updates, reducing communication rounds while preserving data privacy. Across synthetic and real-world (NASA SRTM) datasets, pxpGP and dec-pxpGP achieve accurate hyperparameter estimates and superior predictive uncertainty (lower NLPD) in large networks, with favorable computational and communication complexity compared to existing distributed GP methods.

Abstract

Multi-robot systems require scalable and federated methods to model complex environments under computational and communication constraints. Gaussian Processes (GPs) offer robust probabilistic modeling, but suffer from cubic computational complexity, limiting their applicability in large-scale deployments. To address this challenge, we introduce the pxpGP, a novel distributed GP framework tailored for both centralized and decentralized large-scale multi-robot networks. Our approach leverages sparse variational inference to generate a local compact pseudo-representation. We introduce a sparse variational optimization scheme that bounds local pseudo-datasets and formulate a global scaled proximal-inexact consensus alternating direction method of multipliers (ADMM) with adaptive parameter updates and warm-start initialization. Experiments on synthetic and real-world datasets demonstrate that pxpGP and its decentralized variant, dec-pxpGP, outperform existing distributed GP methods in hyperparameter estimation and prediction accuracy, particularly in large-scale networks.

Figures (5)

• Figure 1: Overview of the proposed pxpGP framework in centralized and decentralized multi-robot networks. Each agent $M_i$ generates a compact pseudo-dataset $\mathcal{D}_i^*$ and forms a pseudo-augmented dataset $\mathcal{D}_{+i}^*$. Centralized networks aggregate pseudo-datasets via a central node, while decentralized networks exchange data through neighbors via flooding.
• Figure 2: Effect of pxpGP regularization. (a) Pseudo-points drift beyond local bounds without boundary penalty (highlighted red circles). (b) Without the repulsive penalty, points cluster densely in a local region (highlighted red circles). (c) Combined boundary ($\mathfrak{L}_{b}$) and repulsive ($\mathfrak{L}_{r}$) penalties yield a well-distributed local pseudo-representations.
• Figure 3: Visualization of the datasets used for experimentation. Figures \ref{['fig:dataset_1']}, \ref{['fig:dataset_2']}, and \ref{['fig:dataset_3']} depict synthetic generative GP datasets used for hyperparameter accuracy evaluation experiments, while Figure \ref{['fig:dataset_4']} and \ref{['fig:dataset_5']} show real-world NASA SRTM terrain datasets farr2007shuttle used for assessing prediction performance.
• Figure 4: Hyperparameter estimation accuracy of baseline GP methods and proposed pxpGP (highlighted with green background) for centralized (black) and decentralized (blue) setups across fleet sizes $M = \left\{ 16, 49, 64, 100 \right\}$ on a dataset with $N = 16{,}900$. Red dashed lines indicate ground-truth hyperparameters.
• Figure 5: Hyperparameter estimation accuracy of baseline GP methods and proposed pxpGP (highlighted with green background) for centralized (black) and decentralized (blue) setups across fleet sizes $M = \left\{ 16, 49, 64, 100 \right\}$ on a dataset with $N = 32{,}400$. Red dashed lines indicate ground-truth hyperparameters.