Zeroth-Order primal-dual Alternating Projection Gradient Algorithms for Nonconvex Minimax Problems with Coupled linear Constraints

In this paper, we study zeroth-order algorithms for nonconvex minimax problems with coupled linear constraints under the deterministic and stochastic settings, which have attracted wide attention in machine learning, signal processing and many other fields in recent years, e.g., adversarial attacks in resource allocation problems and network flow problems etc. We propose two single-loop algorithms, namely the zero-order primal-dual alternating projected gradient (ZO-PDAPG) algorithm and the zero-order regularized momentum primal-dual projected gradient algorithm (ZO-RMPDPG), for solving deterministic and stochastic nonconvex-(strongly) …

adversarial adversarial attacks algorithms attacks attention constraints cs.lg fields gradient linear machine machine learning math.oc minimax paper primal processing projection signal stat.ml stochastic study