  We study a fixed step-size noisy distributed gradient descent algorithm for
solving optimization problems in which the objective is a finite sum of smooth
but possibly non-convex functions. Random perturbations are introduced to the
gradient descent directions at each step to actively evade saddle points. Under
certain regularity conditions, and with a suitable step-size, it is established
that each agent converges to a neighborhood of a local minimizer and the size
of the neighborhood depends on the step-size and the confidence parameter. A
numerical example is presented to illustrate the effectiveness of the random
perturbations in terms of escaping saddle points in fewer iterations than
without the perturbations.
