Federated Incremental Subgradient Method for Convex Bilevel Optimization Problems

TL;DR

This paper introduces a federated incremental subgradient method for convex bilevel optimization problems, addressing scenarios with non-unique inner solutions and demonstrating convergence and practical effectiveness.

Contribution

It proposes a novel federated incremental subgradient algorithm tailored for convex bilevel problems with convergence guarantees.

Findings

Convergence of the proposed algorithm is established under certain assumptions.

Numerical experiments show effectiveness in binary classification and location problems.

Abstract

In this letter, we consider a bilevel optimization problem in which the outer-level objective function is strongly convex, whereas the inner-level problem consists of a finite sum of convex functions. Bilevel optimization problems arise in situations where the inner-level problem does not have a unique solution. This has led to the idea of introducing an outer-level objective function to select a solution with the specific desired properties. We propose an iterative method that combines an incremental algorithm with a broadcast algorithm, both based on the principles of federated learning. Under appropriate assumptions, we establish the convergence results of the proposed algorithm. To demonstrate its performance, we present two numerical examples related to binary classification and a location problem.