Decentralized Randomized Block-Coordinate Frank–Wolfe Algorithms for Submodular Maximization Over Networks

We consider decentralized large-scale continuous submodular constrained optimization problems over networks, where the goal is to maximize a sum of nonconvex functions with diminishing returns property. However, the computations of the projection step and the whole gradient can become prohibitive in high-dimensional constrained optimization problems. For this reason, a decentralized randomized block-coordinate Frank-Wolfe algorithm is proposed for submoduar maximization over networks by local communication and computation, which adopts the randomized block-coordinate descent and the Frank-Wolfe technique. We also show that the proposed algorithm converges to an approximation fact
$(1-e^{-p_{\max }/p_{\min }})$
of the global maximal points at a rate of
$\mathcal {O}(1/T)$
by choosing a suitable stepsize, where
$T$
is the number of iterations. In addition, we confirm the theoretical results by experiments.