On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization
This is an incremental technical report that compiles existing differentiation techniques for bi-level optimization problems in machine learning and computer vision.
The paper tackles the problem of differentiating parameterized argmin and argmax problems, which are common in bi-level optimization, by collecting results and providing motivating examples.
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.