A Polylog Pivot Steps Simplex Algorithm for Classification

Elad Hazan, Zohar Shay Karnin

Abstract: We present a simplex algorithm for linear programming in a linear classification formulation. The paramount complexity parameter in linear classification problems is called the margin. We prove that for margin values of practical interest our simplex variant performs a polylogarithmic number of pivot steps in the worst case, and its overall running time is near linear. This is in contrast to general linear programming, for which no sub-polynomial pivot rule is known.