Fractional Order Distributed Optimization: Theory, Applications, and Empirical Validation

Abstract

Distributed optimization (DO) is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned prob lems and face stability-versus-speed tradeoffs. In this thesis manuscript, we provide a theoretical background on DO and fractional calculus, and introduce fractional order distributed optimization (FrODO) - a theoretically-grounded framework that incorpo rates fractional-order memory terms to enhance convergence properties in challenging optimization landscapes. We provide a convergence proof for our algorithm and show through empirical validation that our algorithm achieves competitive performance with state of the art methodology