Efficient inexact proximal gradient algorithms for structured sparsity-inducing norm

Abstract

Structured-sparsity regularization is popular for sparse learning because of its flexibility of encoding the feature structures. This paper considers a generalized version of structured-sparsity regularization (especially for l1∕l∞ norm) with arbitrary group overlap. Due to the group overlap, it is time-consuming to solve the associated proximal operator. Although Mairal et al. have proposed a network-flow algorithm to solve the proximal operator, it is still time-consuming, especially in the high-dimensional setting. To address this challenge, in this paper, we have developed a more efficient solution for l1∕l∞ group lasso with arbitrary group overlap using inexact proximal gradient method. In each iteration, our algorithm only requires to calculate an inexact solution to the proximal sub-problem, which can be done efficiently. On the theoretic side, the proposed algorithm enjoys the same global convergence rate as the exact proximal methods. Experiments demonstrate that our algorithm is much more efficient than the network-flow algorithm while retaining similar generalization performance.