Projection Free Online Convex Optimization

Projection-free online convex optimization (OCO) aims to solve optimization problems where repeatedly projecting onto a complex feasible set is computationally expensive. Current research focuses on developing algorithms that replace projections with alternative oracles, such as linear optimization or membership oracles, while maintaining near-optimal regret bounds. These methods leverage techniques like Frank-Wolfe variants, Newton iterations with efficient Hessian approximations, and primal-dual approaches to achieve improved efficiency, particularly for high-dimensional problems and time-varying constraints. The resulting algorithms have significant implications for large-scale machine learning and other applications where computationally efficient online learning is crucial.