Decentralized Statistical Inference with Unrolled Graph Neural Networks

TL;DR

This paper introduces a learning-based framework that unrolls decentralized optimization algorithms into graph neural networks, improving convergence speed and recovery accuracy in decentralized statistical inference tasks.

Contribution

It proposes a novel GNN-based approach that addresses model mismatch and enhances convergence in decentralized inference, outperforming traditional optimization algorithms.

Findings

Learned models accelerate convergence.

Reduced recovery error significantly.

Outperforms state-of-the-art algorithms.

Abstract

In this paper, we investigate the decentralized statistical inference problem, where a network of agents cooperatively recover a (structured) vector from private noisy samples without centralized coordination. Existing optimization-based algorithms suffer from issues of model mismatch and poor convergence speed, and thus their performance would be degraded, provided that the number of communication rounds is limited. This motivates us to propose a learning-based framework, which unrolls well-noted decentralized optimization algorithms (e.g., Prox-DGD and PG-EXTRA) into graph neural networks (GNNs). By minimizing the recovery error via end-to-end training, this learning-based framework resolves the model mismatch issue. Our convergence analysis (with PG-EXTRA as the base algorithm) reveals that the learned model parameters may accelerate the convergence and reduce the recovery error to a large extent. The simulation results demonstrate that the proposed GNN-based learning methods prominently outperform several state-of-the-art optimization-based algorithms in convergence speed and recovery error.