Online Power Control for Distributed Multitask Learning Over Noisy Fading Wireless Channels

Distributed (federated) machine learning requires agents, e.g., mobile devices and sensors, to exchange information with a parameter server, leading to substantial communication power consumption. Existing work on power management for distributed learning mainly focuses on single-task learning, where all agents seek to learn a common model. In this paper, we study power control for distributed multitask learning, where agents collaborate to train personalized models and infer their relationships. The agents communicate with a parameter server over noisy fading wireless channels, where information is transmitted imperfectly. We establish the convergence bound for the wireless distributed multitask learning system in terms of the transmission power of the agents. Building upon the convergence bound, we formulate a power control problem, whose goal is to optimize the learning performance under the power constraints of agents. This problem is challenging to solve since only causal information about channel states is available. To resolve this challenge, we resort to the Lyapunov optimization framework and propose an online power control algorithm, where a virtual power queue is constructed and updated at each agent. We analyze the performance of the proposed algorithm and establish \mathcal{O}(\sqrt{T}) dynamic regret bound and \mathcal{O}(\sqrt{T}) power overflow bound, where T is the time horizon. Finally, numerical experiments on real-world datasets demonstrate that the proposed online power control algorithm outperforms existing benchmark schemes while satisfying the power constraints.