Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)
Lee-Ad Gottlieb, Eran Kaufman, Aryeh Kontorovich, Gabriel Nivasch
We present improved algorithm for properly learning convex polytopes in the realizable PAC setting from data with a margin. Our learning algorithm constructs a consistent polytope as an intersection of about t log t halfspaces with margins in time polynomial in t (where t is the number of halfspaces forming an optimal polytope). We also identify distinct generalizations of the notion of margin from hyperplanes to polytopes and investigate how they relate geometrically; this result may be of interest beyond the learning setting.