Decentralized Statistical Inference with Unrolled Graph Neural Networks
This work addresses the issue of model mismatch and slow convergence in decentralized networks for agents cooperatively recovering structured vectors, representing an incremental improvement over existing optimization-based approaches.
The paper tackles the decentralized statistical inference problem by proposing a learning-based framework that unrolls decentralized optimization algorithms into graph neural networks, achieving faster convergence and lower recovery error compared to state-of-the-art optimization-based methods.
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.