Bilevel Toolbox

This is a MATLAB Toolbox designed to test different bilevel optimization problems of the form $ \min_u J(y,u)$

Installation

To use the toolbox, please execute the script init_bilevel_toolbox.m to place all the required scripts into the MATLAB path.

Lower Level Problem

In order to define the lower level problem, we need to create a struct that contains a SOLVE method

% Define lower level problem
lower_level_problem.solve = @(u) solve_lower_level(u);

Upper Level Problem

This struct must contain the following methods:

• GRADIENT: It returns the gradient for a given parameter.
• EVAL: It calculates the cost function for the upper level problem, this function takes a mandatory solution for the lower level problem.
• DATASET: It is an instance of the Dataset class which specifies the training set to be used in the parameter learning problem.

% Define upper level problem
upper_level_problem.eval = @(y,u,zd,alpha) 0.5*norm(y-zd).^2 + 0.5*alpha*norm(u).^2;
upper_level_problem.gradient = @(y,u,zd,alpha) solve_grad_upper_level(y,u,zd,alpha);
upper_level_problem.dataset = dataset;

Bilevel Solver

Once both the upper and lower level problems have been properly defined, we can run the bilevel solver. To call this solver some previous parameter configurations are needed.

bilevel_param.verbose = 2;
bilevel_param.maxit = 1000;
bilevel_param.tol = 1e-5;
bilevel_param.algo = 'NONSMOOTH_TRUST_REGION';
bilevel_param.radius = 0.5;
bilevel_param.minradius = 0.01;
bilevel_param.gamma1 = 0.5;
bilevel_param.gamma2 = 1.5;
bilevel_param.eta1 = 0.10;
bilevel_param.eta2 = 0.90;

% Solve the bilevel problem
[sol,info] = solve_bilevel(u,lower_level_problem,upper_level_problem,bilevel_param);