Efficient Projection-Free Online Methods with Stochastic Recursive Gradient

This paper focuses on projection-free methods for solving smooth Online Convex Optimization (OCO) problems. Existing projection-free methods either achieve suboptimal reg ret bounds or have high per-iteration computational costs. To fi ll this gap, two efficient projection-free online methods call ed ORGFW and MORGFW are proposed for solving stochastic and adversarial OCO problems, respectively. By employing a recursive gradient estimator, our methods achieve optimal regret bounds (up to a logarithmic factor) while possessing low per-iteration computational costs. Experimen tal results demonstrate the efficiency of the proposed methods compared to state-of-the-arts.