  Online learning has been in the spotlight from the machine learning society
for a long time. To handle massive data in Big Data era, one single learner
could never efficiently finish this heavy task. Hence, in this paper, we
propose a novel distributed online learning algorithm to solve the problem.
Comparing to typical centralized online learner, the distributed learners
optimize their own learning parameters based on local data sources and timely
communicate with neighbors. However, communication may lead to a privacy
breach. Thus, we use differential privacy to preserve the privacy of learners,
and study the influence of guaranteeing differential privacy on the utility of
the distributed online learning algorithm. Furthermore, by using the results
from Kakade and Tewari (2009), we use the regret bounds of online learning to
achieve fast convergence rates for offline learning algorithms in distributed
scenarios, which provides tighter utility performance than the existing
state-of-the-art results. In simulation, we demonstrate that the differentially
private offline learning algorithm has high variance, but we can use mini-batch
to improve the performance. Finally, the simulations show that the analytical
results of our proposed theorems are right and our private distributed online
learning algorithm is a general framework.
