Export Reviews, Discussions, Author Feedback and Meta-Reviews

Summary: This paper presents an unprecedentedly fast method for eliminating variables during iterations of multi-task group lasso that is provably safe, meaning that all variables that are eliminated would ultimately obtain zero weights when running vanilla group lasso. This method is iterative; as the primal solver converges, it eliminates an increasing number of variables. The authors compare their method to previous methods and demonstrate that all previous methods are either unsafe or are substantially slower for small duality gaps. The authors describe how their method should be applied to specific cases of group lasso, including l1 and l1/l2 regularized logistic regression, and present real applications where their method achieves a substantial speed-up over vanilla group lasso and an existing method for small duality gap thresholds. The primary situation where this method obtains substantial speed improvements over alternatives is where the duality gap threshold is extremely small.