  Designing policies for a network of agents is typically done by formulating
an optimization problem where each agent has access to state measurements of
all the other agents in the network. Such policy designs with centralized
information exchange result in optimization problems that are typically hard to
solve, require establishing substantial communication links, and do not promote
privacy since all information is shared among the agents. Designing policies
based on arbitrary communication structures can lead to non-convex optimization
problems which are typically NP-hard. In this work, we propose an optimization
framework for decentralized policy designs. In contrast to the centralized
information exchange, our approach requires only local communication exchange
among the neighboring agents matching the physical coupling of the network.
Thus, each agent only requires information from its direct neighbors,
minimizing the need for excessive communication and promoting privacy amongst
the agents. Using robust optimization techniques, we formulate a convex
optimization problem with a loosely coupled structure that can be solved
efficiently. We numerically demonstrate the efficacy of the proposed approach
in energy management and supply chain applications. We show that the proposed
approach leads to solutions that closely approximate those obtained by the
centralized formulation only at a fraction of the computational effort.
