Exact asymptotic characterisation of running time for approximate gradient descent on random graphs

Manuel Saenz, Matthieu Jonckheere

Abstract: In this work we study the time complexity for the search of local minima in random graphs whose vertices have i.i.d. cost values. We show that, for Erdos-Renyi graphs with connection probability given by a family of local algorithms that approximate a gradient descent find local minima faster than the full gradient descent. Furthermore, we find a probabilistic representation for the running time of these algorithms leading to asymptotic estimates of the mean running times.