A First Order Method for Solving Convex Bilevel Optimization Problems

By Shoham Sabach, Shimrit Shtern. 2017

225 citations recorded by the source corpus.

In this paper we study convex bilevel 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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Ruichen Jiang
2. Nazanin Abolfazli
3. Aryan Mokhtari
4. Nathan Kallus
5. Erfan Yazdandoost Hamedani
6. Alejandro Ribeiro

In Computational Theory and Mathematics

1. Ruichen Jiang
2. Nazanin Abolfazli
3. Aryan Mokhtari
4. Nathan Kallus
5. Erfan Yazdandoost Hamedani
6. Andrew Bennett

In Numerical Analysis

1. Ruichen Jiang
2. Nazanin Abolfazli
3. Aryan Mokhtari
4. Nathan Kallus
5. Erfan Yazdandoost Hamedani

Citations in the corpus

• Balanced Policy Evaluation and Learning (2017, methodology): “This is a limitation of the current optimization algorithm that we hope to improve on in the future using specialized methods for bilevel optimization [4, 32, 37].”
• A Conditional Gradient-based Method for Simple Bilevel Optimization with Convex Lower-level Problem (2022, methodology): “For BiG-SAM, we set ηf = ηg = 0.1 and γ = 10.”