Decentralized Learning Strategies for Estimation Error Minimization with Graph Neural Networks
CoRR(2024)
摘要
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.
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