  In this paper, we consider the problem of power control for a wireless
network with an arbitrarily time-varying topology, including the possible
addition or removal of nodes. A data-driven design methodology that leverages
graph neural networks (GNNs) is adopted in order to efficiently parametrize the
power control policy mapping the channel state information (CSI) to transmit
powers. The specific GNN architecture, known as random edge GNN (REGNN),
defines a non-linear graph convolutional filter whose spatial weights are tied
to the channel coefficients. While prior work assumed a joint training approach
whereby the REGNN-based policy is shared across all topologies, this paper
targets adaptation of the power control policy based on limited CSI data
regarding the current topology. To this end, we propose a novel modular
meta-learning technique that enables the efficient optimization of module
assignment. While black-box meta-learning optimizes a general-purpose
adaptation procedure via (stochastic) gradient descent, modular meta-learning
finds a set of reusable modules that can form components of a solution for any
new network topology. Numerical results validate the benefits of meta-learning
for power control problems over joint training schemes, and demonstrate the
advantages of modular meta-learning when data availability is extremely
limited.
