Adaptive Proximal Algorithms for Convex Simple Bilevel optimization

This repository contains Julia code for the paper AdaBiM: An essentially adaptive proximal gradient method for convex simple bilevel optimization.

The problems that can be tackled are of the form

$$ \begin{aligned} \text{minimize} \quad & f^1(x) + g^1(x) \\ \text{subject to} \quad & x \in \arg\min_{w} f^2(w) + g^2(w) \end{aligned} $$

where $f^1,f^2$ are locally Lipschitz differentiable and $g^1,g^2$ are (possibly) nonsmooth prox-friendly functions.

Algorithms are implemented here.

You can download the datasets required in some of the experiments by running:

julia --project=. download_datasets.jl

Numerical simulations for a few different problems are contained in subfolders. For example, the linear inverse problem with the $\ell_1$ norm as the upper-level cost function can be found here. The runme.jl file includes the associated simulations. Executing main() will generate the plots in the same subfolder.