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2016

A deterministic rescaled perceptron algorithm

4 years 2 months ago
A deterministic rescaled perceptron algorithm
The perceptron algorithm is a simple iterative procedure for finding a point in a convex cone F. At each iteration, the algorithm only involves a query to a separation oracle for F and a simple update on a trial solution. The perceptron algorithm is guaranteed to find a point in F after O(1/τ2 F ) iterations, where τF is the width of the cone F. We propose a version of the perceptron algorithm that includes a periodic rescaling of the ambient space. In contrast to the classical version, our rescaled version finds a point in F in O(m5 log(1/τF )) perceptron updates. This result is inspired by and strengthens the previous work on randomized rescaling of the perceptron algorithm by Dunagan and Vempala [Math. Program. 114 (2006), 101–114] and by Belloni, Freund, and Vempala [Math. Oper. Res. 34 (2009), 621–641]. In particular, our algorithm and its complexity analysis are simpler and shorter. Furthermore, our algorithm does not require randomization or deep separation oracles.
Javier Peña, Negar Soheili
Added 08 Apr 2016
Updated 08 Apr 2016
Type Journal
Year 2016
Where MP
Authors Javier Peña, Negar Soheili
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