Implicit differentiation for hyperparameter optimization of Lasso-type models

Jul 12, 2020

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Setting regularization parameters for Lasso-type estimators is notoriously difficult, though crucial for obtaining the best accuracy. The most popular hyperparameter optimization approach is grid-search on a held-out dataset. However, grid-search requires to choose a predefined grid of parameters and scales exponentially in the number of parameters. Another class of approaches casts hyperparameter optimization as a bi-level optimization problem, typically solved by gradient descent. The key challenge for these approaches is the estimation of the gradient w.r.t. the hyperparameters. Computing that gradient via forward or backward automatic differentiation usually suffers from high memory comsumption, while implicit differentiation typically involves solving a linear system which can be prohibitive and numerically unstable. In addition, implicit differentiation usually assumes smooth loss functions, which is not the case of Lasso-type problems. This work introduces an efficient implicit differentiation algorithm, without matrix inversion, tailored for Lasso-type problems. Our proposal scales to high-dimensional data by leveraging the sparsity of the solutions. Empirically, we demonstrate that the proposed method outperforms a large number of standard methods for hyperparameter optimization.

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The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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