  Online meta-learning is emerging as an enabling technique for achieving edge
intelligence in the IoT ecosystem. Nevertheless, to learn a good meta-model for
within-task fast adaptation, a single agent alone has to learn over many tasks,
and this is the so-called 'cold-start' problem. Observing that in a multi-agent
network the learning tasks across different agents often share some model
similarity, we ask the following fundamental question: "Is it possible to
accelerate the online meta-learning across agents via limited communication and
if yes how much benefit can be achieved? " To answer this question, we propose
a multi-agent online meta-learning framework and cast it as an equivalent
two-level nested online convex optimization (OCO) problem. By characterizing
the upper bound of the agent-task-averaged regret, we show that the performance
of multi-agent online meta-learning depends heavily on how much an agent can
benefit from the distributed network-level OCO for meta-model updates via
limited communication, which however is not well understood. To tackle this
challenge, we devise a distributed online gradient descent algorithm with
gradient tracking where each agent tracks the global gradient using only one
communication step with its neighbors per iteration, and it results in an
average regret $O(\sqrt{T/N})$ per agent, indicating that a factor of
$\sqrt{1/N}$ speedup over the optimal single-agent regret $O(\sqrt{T})$ after
$T$ iterations, where $N$ is the number of agents. Building on this sharp
performance speedup, we next develop a multi-agent online meta-learning
algorithm and show that it can achieve the optimal task-average regret at a
faster rate of $O(1/\sqrt{NT})$ via limited communication, compared to
single-agent online meta-learning. Extensive experiments corroborate the
theoretic results.
