  Conventional online multi-task learning algorithms suffer from two critical
limitations: 1) Heavy communication caused by delivering high velocity of
sequential data to a central machine; 2) Expensive runtime complexity for
building task relatedness. To address these issues, in this paper we consider a
setting where multiple tasks are geographically located in different places,
where one task can synchronize data with others to leverage knowledge of
related tasks. Specifically, we propose an adaptive primal-dual algorithm,
which not only captures task-specific noise in adversarial learning but also
carries out a projection-free update with runtime efficiency. Moreover, our
model is well-suited to decentralized periodic-connected tasks as it allows the
energy-starved or bandwidth-constraint tasks to postpone the update.
Theoretical results demonstrate the convergence guarantee of our distributed
algorithm with an optimal regret. Empirical results confirm that the proposed
model is highly effective on various real-world datasets.
