  Some recent works in machine learning and computer vision involve the
solution of a bi-level optimization problem. Here the solution of a
parameterized lower-level problem binds variables that appear in the objective
of an upper-level problem. The lower-level problem typically appears as an
argmin or argmax optimization problem. Many techniques have been proposed to
solve bi-level optimization problems, including gradient descent, which is
popular with current end-to-end learning approaches. In this technical report
we collect some results on differentiating argmin and argmax optimization
problems with and without constraints and provide some insightful motivating
examples.

Computer Vision and Pattern Recognition;Optimization and Control