Exact characterisation of asymptotic running time for approximate gradient descent on random graphs
Matthieu Jonckheere, Manuel Sáenz · Stochastic Analysis and Applications · 2025
.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 Erdös-Rényi graphs with connection probability given by λ∕nα (with λ > 0 and 0<α<1), 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.