  We study the privatization of distributed learning and optimization
strategies. We focus on differential privacy schemes and study their effect on
performance. We show that the popular additive random perturbation scheme
degrades performance because it is not well-tuned to the graph structure. For
this reason, we exploit two alternative graph-homomorphic constructions and
show that they improve performance while guaranteeing privacy. Moreover,
contrary to most earlier studies, the gradient of the risks is not assumed to
be bounded (a condition that rarely holds in practice; e.g., quadratic risk).
We avoid this condition and still devise a differentially private scheme with
high probability. We examine optimization and learning scenarios and illustrate
the theoretical findings through simulations.
