  We propose a throughput-optimal biased backpressure (BP) algorithm for
routing, where the bias is learned through a graph neural network that seeks to
minimize end-to-end delay. Classical BP routing provides a simple yet powerful
distributed solution for resource allocation in wireless multi-hop networks but
has poor delay performance. A low-cost approach to improve this delay
performance is to favor shorter paths by incorporating pre-defined biases in
the BP computation, such as a bias based on the shortest path (hop) distance to
the destination. In this work, we improve upon the widely-used metric of hop
distance (and its variants) for the shortest path bias by introducing a bias
based on the link duty cycle, which we predict using a graph convolutional
neural network. Numerical results show that our approach can improve the delay
performance compared to classical BP and existing BP alternatives based on
pre-defined bias while being adaptive to interference density. In terms of
complexity, our distributed implementation only introduces a one-time overhead
(linear in the number of devices in the network) compared to classical BP, and
a constant overhead compared to the lowest-complexity existing bias-based BP
algorithms.
