Box-constrained L0 Bregman-relaxations

Abstract

Regularization using the L0 pseudo-norm is a common approach to promote sparsity, with widespread applications in machine learning and signal processing. However, solving such problems is known to be NP-hard. Recently, the L0 Bregman relaxation (B-rex) has been introduced as a continuous, non-convex approximation of the L0 pseudo-norm. Replacing the L0 term with B-rex leads to exact continuous relaxations that preserve the global optimum while simplifying the optimization landscape, making non-convex problems more tractable for algorithmic approaches. In this paper, we focus on box-constrained exact continuous Bregman relaxations of L0-regularized criteria with general data terms, including least-squares, logistic regression, and Kullback-Leibler fidelities. Experimental results on synthetic data, compared with Branch-and-Bound methods, demonstrate the effectiveness of the proposed relaxations.