# On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization

arXiv: https://arxiv.org/abs/1607.05447 · HTML: https://mlsanity.com/paper/1607.05447/

## Key facts

- Cited by 112 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2016.

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## Abstract (arXiv)

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.