Decentralized Statistical Inference with Unrolled Graph Neural Networks
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 optimizationbased 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 toend 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.
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