Decentralized Randomized Block-Coordinate Frank–Wolfe Algorithms for Submodular Maximization Over Networks
Mingchuan Zhang, Yangfan Zhou, Quanbo Ge, Ruijuan Zheng, Qingtao Wu · IEEE Transactions on Systems Man and Cybernetics Systems · 2021
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.