Decentralized Learning Strategies for Estimation Error Minimization with
  Graph Neural Networks
Xingran Chen Navid NaderiAlizadeh Alejandro Ribeiro Shirin Saeedi Bidokhti
We address the challenge of sampling and remote estimation for autoregressive
Markovian processes in a multi-hop wireless network with
statistically-identical agents. Agents cache the most recent samples from
others and communicate over wireless collision channels governed by an
underlying graph topology. Our goal is to minimize time-average estimation
error and/or age of information with decentralized scalable sampling and
transmission policies, considering both oblivious (where decision-making is
independent of the physical processes) and non-oblivious policies (where
decision-making depends on physical processes). We prove that in oblivious
policies, minimizing estimation error is equivalent to minimizing the age of
information. The complexity of the problem, especially the multi-dimensional
action spaces and arbitrary network topologies, makes theoretical methods for
finding optimal transmission policies intractable. We optimize the policies
using a graphical multi-agent reinforcement learning framework, where each
agent employs a permutation-equivariant graph neural network architecture.
Theoretically, we prove that our proposed framework exhibits desirable
transferability properties, allowing transmission policies trained on small- or
moderate-size networks to be executed effectively on large-scale topologies.
Numerical experiments demonstrate that (i) Our proposed framework outperforms
state-of-the-art baselines; (ii) The trained policies are transferable to
larger networks, and their performance gains increase with the number of
agents; (iii) The training procedure withstands non-stationarity even if we
utilize independent learning techniques; and, (iv) Recurrence is pivotal in
both independent learning and centralized training and decentralized execution,
and improves the resilience to non-stationarity in independent learning.