  Inventory control is subject to service-level requirements, in which
sufficient stock levels must be maintained despite an unknown demand. We
propose a data-driven order policy that certifies any prescribed service level
under minimal assumptions on the unknown demand process. The policy achieves
this using any online learning method along with integral action. We further
propose an inference method that is valid in finite samples. The properties and
theoretical guarantees of the method are illustrated using both synthetic and
real-world data.
