Uncertain multi-agent MILPs: A data-driven decentralized solution with probabilistic feasibility guarantees

We consider uncertain multi-agent optimization problems that are formulated as Mixed Integer Linear Programs (MILPs) with an almost separable structure. Specifically, agents have their own cost function and constraints, and need to set their local decision vector subject to coupling constraints due to shared resources. The problem is affected by uncertainty that is only known from data. A scalable decentralized approach to tackle the combinatorial complexity of constraint-coupled multi-agent MILPs has been recently introduced in the literature. However, the presence of uncertainty has been addressed only in a distributed convex optimization framework, i.e., without integer decision variables. This work fills in this gap by proposing a data-driven decentralized scheme to determine a solution with probabilistic feasibility guarantees that depend on the size of the data-set.