Projection-free Online Learning over Strongly Convex Sets

To efficiently solve online problems with complicated constraints, projection-free algorithms including frank-wolfe (OFW) and its variants have received significant interest recently. However, in the general case, existing efficient only achieved regret bound of O(T^{3/4}), which is worse than projection-based algorithms, where T number decision rounds. In this paper, we study special case learning over strongly convex sets, for first prove that OFW can enjoy a better O(T^{2/3}) losses. The key idea to refine decaying step-size original by simple line search rule. Furthermore, losses, propose variant redefining surrogate loss function OFW. We show it achieves sets O(T^{1/2}) sets.