This paper considers distributed online convex constrained optimization, in which various agents in a multi-agent system cooperate to minimize a global cost function through communicating with neighbors over a time-varying network. When the constraint set of optimization problem is high-dimensional and complicated, the computational cost of the projection operation often becomes prohibitive. To handle this problem, we develop a distributed online Frank-Wolfe optimization algorithm combining with gradient tracking technique. We rigorously establish the dynamic regret bound of the proposed optimization algorithm as O(T(1+HT)+DT), which explicitly depends on the iteration round T, function variation HT, and gradient variation DT. Finally, the theoretical results are verified and compared in the case of distributed online ridge regression problems.
@article{arxiv.2302.00663,
title = {Dynamic Regret of Distributed Online Frank-Wolfe Convex Optimization},
author = {Wentao Zhang and Yang Shi and Baoyong Zhang and Deming Yuan},
journal= {arXiv preprint arXiv:2302.00663},
year = {2023}
}