Decentralized nonconvex optimization with guaranteed privacy and accuracy

Privacy protection and nonconvexity are two challenging problems in decentralized optimization learning involving sensitive data. Despite some recent advances addressing each of the separately, no results have been reported that theoretical guarantees on both privacy saddle/maximum avoidance nonconvex optimization. We propose a new algorithm for can enable rigorous differential avoiding performance. The allows incorporation persistent additive noise to data samples, gradients, intermediate variables without losing provable convergence, thus circumventing dilemma trading accuracy design. More interestingly, is theoretically proven be able efficiently guarantee by convergence local maxima saddle points, which has not before literature efficient communication (it only shares one variable iteration) computation encryption-free), hence promising large-scale high-dimensional parameters. Numerical experiments estimation problem an Independent Component Analysis (ICA) confirm effectiveness proposed approach.