Inverse Feasibility in Over-the-Air Federated Learning

TL;DR

This paper introduces inverse feasibility, a new concept based on inverse problem theory, to improve over-the-air federated learning models by analyzing and optimizing the condition number of the forward operator.

Contribution

It defines inverse feasibility for OTA FL, analyzes existing models, and proposes a new model to enhance performance and security features.

Findings

Inverse feasibility bounds the condition number of the forward operator.

Analysis reveals areas for improvement in existing OTA FL models.

Numerical experiments validate the theoretical insights.

Abstract

We introduce the concept of inverse feasibility for linear forward models as a tool to enhance OTA 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.