A Linearly Convergent Projection-Free Algorithm for Smooth Convex Sets

What the math gives to ML

The paper gives a constructive way to obtain geometric convergence without projections or linear-optimization oracles when the feasible set has a rolling-ball smoothness condition. Its transferable asset is an approximate local linear minimization primitive: solve a linear objective over a ball intersected with one supporting halfspace, then repair the result using a tangent estimate, with only an additive error proportional to the squared locality radius. This is most promising for constrained neural subproblems such as convex last-layer training, low-dimensional adapter optimization, or norm-constrained fine-tuning, where exact projection is expensive but membership and boundary-normal queries are cheap.