Wide and Deep Graph Neural Networks with Distributed Online Learning
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Graph neural networks (GNNs) learn representations from network data with naturally distributed architectures. This renders them well-suited candidates for decentralized learning since the operations respect the structure imposed by the underlying graph. Oftentimes, this graph support changes with time, whether it is due to link failures or topology changes caused by mobile components. Modifications to the underlying structure create a mismatch between the graphs on which GNNs were trained and the ones on which they are tested. Online learning can be used to retrain the GNNs at test time, overcoming this issue. However, most online learning algorithms are centralized and work on convex objective functions (which GNNs rarely lead to). This paper puts forth the Wide and Deep GNN (WD-GNN), a novel architecture that can be easily updated with distributed online learning mechanisms. The WD-GNN consists of two components: the wide part is a bank of linear graph filters and the deep part is a convolutional GNN. At training time, the joint architecture learns a relevant nonlinear representation from data. At test time, the deep part is left unchanged, while the wide part is retrained online. Since the wide part is linear, the problem becomes convex, and online optimization algorithms can be used. We also propose a distributed online optimization algorithm that updates the wide part at test time, without violating its decentralized nature. We also analyze the stability of the WD-GNN to changes in the underlying topology and derive convergence guarantees for the online retraining procedure. These results indicate the transferability, scalability, and efficiency of the WD-GNN to adapt online to new testing scenarios in a distributed manner. Experiments on the control of robot swarms corroborate the theory and show the potential of the proposed architecture for distributed online learning.
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