Export Reviews, Discussions, Author Feedback and Meta-Reviews

This paper considers efficient implementations of non-convex sparse learning formulations. Recent studies have shown that many convex sparse learning formulations are inferior to their non-convex counterparts in both theory and practice. However, it is still quite challenging to efficiently solve non-convex sparse optimization problems for large-scale data. This paper presents a novel algorithm HONOR which is applicable for a wide range of non-convex sparse learning formulations. One of the key ideas in HONOR is to incorporate the second-order information to greatly speed up the convergence, while unlike most existing second-order methods it avoids solving a regularized quadratic programming and only involves matrix-vector multiplications without explicitly forming the inverse Hessian matrix. Thus, HONOR has a low computational complexity at each iteration and it is scalable to large-size problems.