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

Alessandro Falsone, Federico Molinari, Maria Prandini

Abstract: 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. We introduce a data-driven decentralized scheme for handling the combinatorial complexity of the resulting MILP, while providing a probabilistic feasibility certificate that depends on the size of the data-set. The proposed approach rests on a decentralized multi-agent MILP resolution algorithm recently introduced in the literature, which is extended here to an uncertain framework by using tools from statistical learning theory.