Inverse Feasibility in Over-the-Air Federated Learning

We introduce the concept of inverse feasibility for linear forward models as a tool to enhance Over-the-Air (OTA) federated learning (FL) algorithms. Inverse feasibility is defined as an upper bound on the condition number of the forward operator as a function of its parameters. We analyze an existing OTA FL model using this definition, identify areas for improvement, and propose a new OTA FL model. Numerical experiments illustrate the main implications of the theoretical results. The proposed framework, which is based on inverse problem theory, can potentially complement existing notions of security and privacy by providing additional desirable characteristics to networks.