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Safe Grid Search with Optimal Complexity
Eugene Ndiaye · Tam Le · Olivier Fercoq · Joseph Salmon · Ichiro Takeuchi

Tue Jun 11 03:10 PM -- 03:15 PM (PDT) @ Room 103
Popular machine learning estimators involve regularization parameters that can be challenging to tune, and standard strategies rely on grid search for this task. In this paper, we revisit the techniques of approximating the regularization path up to predefined tolerance $\epsilon$ in a unified framework and show that its complexity is $O(1/\sqrt[d]{\epsilon})$ for uniformly convex loss of order $d>0$ and $O(1/\sqrt{\epsilon})$ for Generalized Self-Concordant functions. This framework encompasses least-squares but also logistic regression, a case that as far as we know was not handled as precisely in previous works. We leverage our technique to provide refined bounds on the validation error as well as a practical algorithm for hyperparameter tuning. The later has global convergence guarantee when targeting a prescribed accuracy on the validation set. Last but not least, our approach helps relieving the practitioner from the (often neglected) task of selecting a stopping criterion when optimizing over the training set: our method automatically calibrates this criterion based on the targeted accuracy on the validation set.

Author Information

Eugene Ndiaye (RIKEN AIP)

My name is Tam Le. I have been an assistant professor at The Institute of Statistical Mathematics (ISM), Japan since 09/2022. I am also a visiting scientist at RIKEN AIP, Japan since 12/2022. I officially received my PhD degree from Kyoto University in 01/2016, under the supervision of Professor Marco Cuturi and Professor Akihiro Yamamoto. Before ISM, I worked at RIKEN AIP as a postdoc (09/2017 - 07/2021), and as a research scientist (08/2021 - 08/2022), working with Professor Makoto Yamada. Before those, I spent 1.5 year as a postdoc at Nagoya Institute of Technology and National Institute of Materials Science (02/2016 - 08/2017), working with Professor Ichiro Takeuchi.

Olivier Fercoq (Télécom ParisTech, Université Paris-Saclay)
Joseph Salmon (Université de Montpellier)
Ichiro Takeuchi (Nagoya Institute of Technology / RIKEN)

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