A First Order Method for Solving Convex Bi-Level Optimization Problems

TL;DR

This paper introduces a first-order method for convex bi-level optimization problems, providing convergence analysis and applicable to problems with smooth and nonsmooth inner objectives.

Contribution

It proposes a novel first-order algorithm for convex bi-level problems with convergence guarantees, extending existing fixed-point methods.

Findings

Global sublinear convergence rate established

Method effectively handles smooth and nonsmooth inner functions

Applicable to strongly convex outer functions

Abstract

In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the optimal solutions set of the inner problem. We analyze a first order method which is based on an existing fixed-point algorithm. Global sublinear rate of convergence of the method is established in terms of the inner objective function values.