Learning convex polytopes with margin release_sgtpg3ijxbci5p63uppuk2haue

Abstract

We present an 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 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.
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