The consensus of the reviewers, after rebuttal and discussion, was to accept this paper for NeurIPS. The paper presents an interesting new algorithm that addresses some lingering issues in the application of the conditional gradient method when the constraint set is an unbounded cone. The contribution was decided to be worth publishing in NeurIPS, however, the paper can be improved along the lines suggested by the reviewers, especially to provide more evidence of the superiority of the algorithm to other known approaches. The authors are encouraged to address these comments.