Optimization II Winter 2009 / 10 Lecture 5 — November 9

In this lecture we present a procedure which can be thought of as a derandomization of the randomized fictitious play described in the previous lecture. Freund and Schapire [FS99] used this method, which was originally developed by Littlestone and Warmuth [LW94] from the machine learning community, to give a procedure for computing εsaddle points for matrix games. A number of similar algorithms have also been developed for approximately solving special optimization problems, such as general linear programs [PST91], multicommodity flows problems [GK98], packing and covering linear programs [PST91, GK98, GK04, KY07, You01], some class of convex programs [Kha04], and semidefinite programs [AHK05, AK07]. Arora, Hazan and Kale [AHK06] gave a meta algorithm that puts many of these results under one umbrella. We will partly follow their presentation in this lecture.