Generalized self-concordant analysis of Frank–Wolfe algorithms

Abstract Projection-free optimization via different variants of the Frank–Wolfe method has become one cornerstones large scale for machine learning and computational statistics. Numerous applications within these fields involve minimization functions with self-concordance like properties. Such generalized self-concordant do not necessarily feature a Lipschitz continuous gradient, nor are they strongly convex, making them challenging class first-order methods. Indeed, in number applications, such as inverse covariance estimation or distance-weighted discrimination problems binary classification, loss is given by function having potentially unbounded curvature. For projection-free methods have no theoretical convergence guarantee. This paper closes this apparent gap literature developing provably convergent algorithms standard $$\mathcal {O}(1/k)$$ O ( 1 / k ) rate guarantees. Based on new insights, we show how sublinearly can be accelerated to yield linearly methods, either relying availability local liner oracle, suitable modification away-step method.