On Distributed Stochastic Gradient Algorithms for Global Optimization

Abstract: The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by adding slowly decaying Gaussian noise in order escape local minima. However, the technical assumptions under which convergence is known to occur can be restrictive in practice. In particular, in known convergence results, the local objective functions possessed by agents are required to satisfy a highly restrictive bounded-gradient-dissimilarity condition. The paper demonstrates convergence to the set of global minima while relaxing this key assumption.