Bilevel Optimization and Machine Learning

By Kristin P. Bennett, Gautam Kunapuli, Jing Hu, Jong-Shi Pang. 2008

70 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Numerical Analysis

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Nathan Kallus
2. Thomas Pock
3. Kalyanmoy Deb
4. Thomas Brox
5. Peter Ochs
6. Pekka Malo
7. Ankur Sinha
8. René Ranftl

In Management Science and Operations Research

1. Nathan Kallus
2. Kalyanmoy Deb
3. Alexander R. Statnikov
4. Thomas Brox
5. Thomas Pock
6. Hugo Jair Escalante
7. Isabelle M Guyon
8. Tom Goldstein

In Numerical Analysis

1. Nathan Kallus
2. Thomas Brox
3. Peter Ochs
4. René Ranftl
5. Kalyanmoy Deb
6. Thomas Pock
7. Hugo Jair Escalante
8. Isabelle M Guyon

Citations in the corpus

• Balanced Policy Evaluation and Learning (2017, methodology): “This is a limitation of the current optimization algorithm that we hope to improve on in the future using specialized methods for bilevel optimization [4, 32, 37].”
• MetaPoison: Practical General-purpose Clean-label Data Poisoning (2020, methodology): “, 2012, Bennett et al., 2008], with the higher-level objective of minimizing adversarial loss on target images depending on the lower-level objective of minimizing training loss on poisoned data. This formulation is used to generate poisoned data for SVMs [Biggio et al., 2012], logistic regression [”
• A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications (2017, background): “Some of the approaches that have acknowledged the bilevel nature of this problem are [23], [24], [104], and [154].”
• Techniques for Gradient-Based Bilevel Optimization with Non-smooth Lower Level Problems (2016, methodology): “In machine learning bilevel optimization was used to train a SVM [3] and other techniques [26].”
• Analysis of the AutoML Challenge Series 2015-2018 (2019, methodology): “Efforts have been made to optimize continuous hyper-parameters with bilevel optimization methods, using either the k-fold cross-validation estimator (Bennett et al., 2008; Moore et al., 2011) or the leave-one-out estimator as the upperlevel objective J2.”
• Design of the 2015 ChaLearn AutoML challenge (2015, methodology): “Other embedded methods jointly optimize parameters and hyperparameters [34]–[36], [45], [49].”