Stochastic optimization. Choice of perturbation laws. Application to the itineris network.

Summary Both the stochastic gradient algorithm and the simulated annealing are perturbations of local descent algorithms. Our theoretical analysis of the unconstrained stochastic gradient with Gaussian and Cauchy perturbations shows that in both cases a correct decay of the parameters ensures an efficient exploration, with different application domains: the second variant is less precise but faster, and thus adapted to problems of moderate complexity. The second part of this paper illustrates this discussion with an application to the optimization of the itineris cellular telephone network: an implementation based on simulated annealing is compared with a variant where the exponentially decaying metropolis transition law is replaced by a slower decaying transition law.