a1519de5b5d44b31a01de013b9b51a80-Reviews.html

This paper presents "Sparse Overlapping Sets" Lasso (SOSlasso), a new penalty function for sparse multi-task learning (MTL), whose expression contains both the \ell_1 norm and the group norm penalty that allows groups to overlap. The SOSlasso is motivated by the fact that the commonly used group lasso may not be appropriate when there is uncertainty in the feature correspondence across tasks, and the proposed penalty allows one to strike a balance between two extremes: (1) lasso, where task similarity is not exploited in any way, and (2) the group lasso, which rigidly groups potentially misaligned features across tasks. By demonstrating that the proposed penalty function is a valid norm which is decomposable with respect to the model subspace of interest, the authors are able to apply the results from the work of Negahban et al. in [9] to prove error bounds for convex and differentiable loss satisfying the restricted strong convexity conditions, as well as consistency for the squared error loss. To apply the results from [9], suitable upperbounds are introduced for the SOSlasso penalty and its dual, which are used to bound the subspace compatibility constant and the dual norm of the gradient of the loss function respectively. Overall, although the paper does not stand out to be revolutionary, it is very well written and offers a natural and valuable extension to the group lasso penalty for sparse MTL.