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Accelerating Distributed Online Meta-Learning via Multi-Agent Collaboration under Limited Communication

Sen Lin, Mehmet Dedeoglu, Junshan Zhang

Thanks to the fast learning capability of a new task with small datasets,
online meta-learning has become an appealing technique for enabling edge
computing in the IoT ecosystems. Nevertheless, to learn a good meta-model for
within-task fast adaptation, a single agent alone has to learn over many tasks,
inevitably leading to the cold-start problem. Seeing that in a multi-agent
network the learning tasks across different agents often share some model
similarity, a fundamental question to ask is "Is it possible to accelerate the
online meta-learning at each agent via limited communication and if yes how
much benefit can be achieved?" To answer this, we propose a multi-agent online
meta-learning framework and treat 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 ceiling of the
multi-agent online meta-learning heavily depends on how much an agent can
benefit from distributed network-level OCO via limited communication, which
however remains unclear. To tackle this challenge, we further study a
distributed online gradient descent algorithm with gradient tracking where
agents collaboratively track the global gradient through only one communication
step per iteration, and it results in $O(\sqrt{T/N})$ for the average regret
per agent, i.e., a factor of $\sqrt{1/N}$ speedup compared with 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.

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