  In this paper, we present a distributed algorithm for solving convex,
constraint-coupled, optimization problems over peer-to-peer networks. We
consider a network of processors that aim to cooperatively minimize the sum of
local cost functions, subject to individual constraints and to global coupling
constraints. The major assumption of this work is that the cost functions are
unknown and must be learned online. We propose a fully distributed algorithm,
based on a primal decomposition approach, that uses iteratively refined
data-driven estimations of the cost functions over the iterations. The
algorithm is scalable and maintains private information of agents. We prove
that, asymptotically, the distributed algorithm provides the optimal solution
of the problem even though the true cost functions are never used within the
algorithm. The analysis requires an in-depth exploration of the primal
decomposition approach and shows that the distributed algorithm can be thought
of as an epsilon-subgradient method applied to a suitable reformulation of the
original problem. Finally, numerical computations cor- roborate the theoretical
findings and show the efficacy of the proposed approach.
