Learning step sizes for unfolded sparse coding

Pierre Ablin (1) , Thomas Moreau (1) , Mathurin Massias (1) , Alexandre Gramfort (1)

1 PARIETAL - Modelling brain structure, function and variability based on high-field MRI data

Sparse coding is typically solved by iterative optimization techniques, such as the Iterative Shrinkage-Thresholding Algorithm (ISTA). Unfolding and learning weights of ISTA using neural networks is a practical way to accelerate estimation. In this paper, we study the selection of adapted step sizes for ISTA. We show that a simple step size strategy can improve the convergence rate of ISTA by leveraging the sparsity of the iterates. However, it is impractical in most large-scale applications. Therefore, we propose a network architecture where only the step sizes of ISTA are learned. We demonstrate that for a large class of unfolded algorithms, if the algorithm converges to the solution of the Lasso, its last layers correspond to ISTA with learned step sizes. Experiments show that our method is competitive with state-of-the-art networks when the solutions are sparse enough.

Domaines: Machine Learning [stat.ML]

Pierre Ablin, Thomas Moreau, Mathurin Massias, Alexandre Gramfort. Learning step sizes for unfolded sparse coding. NeurIPS 2019 - Advances in Neural Information Processing Systems, Dec 2019, Vancouver, Canada. ⟨hal-02140383⟩