An Efficient Re-scaled Perceptron Algorithm for Conic Systems

Abstract. The classical perceptron algorithm is an elementary algorithm for solving a homogeneous linear inequality system Ax > 0, with many important applications in learning theory (e.g., [11, 8]). A natural condition measure associated with this algorithm is the Euclidean width of the cone of feasible solutions, and the iteration complexity of the perceptron algorithm is bounded by 1/2 . Dunagan and Vempala [5] have developed a re-scaled version of the perceptron algorithm with an improved complexity of O(n ln(1/)) iterations (with high probability), which is theoretically efficient in , and in particular is polynomialtime in the bit-length model. We explore extensions of the concepts of these perceptron methods to the general homogeneous conic system Ax int K where K is a regular convex cone. We provide a conic extension of the re-scaled perceptron algorithm based on the notion of a deep-separation oracle of a cone, which essentially computes a certificate of strong separation...

• Type: Conference
• Year: 2007
• Where: COLT
• Authors: Alexandre Belloni, Robert M. Freund, Santosh Vempala
• Keywords: Classical Perceptron Algorithm, COLT 2007, Machine Learning, Perceptron Algorithm, Re-scaled Perceptron Algorithm