 
Summary: The Multiplicative Weights Update Method: a
Meta Algorithm and Applications
Sanjeev Arora
Elad Hazan Satyen Kale
Abstract
Algorithms in varied fields use the idea of maintaining a distribution
over a certain set and use the multiplicative update rule to iteratively
change these weights. Their analysis are usually very similar and rely
on an exponential potential function.
We present a simple meta algorithm that unifies these disparate
algorithms and drives them as simple instantiations of the meta algo
rithm.
1 Introduction
Algorithms in varied fields work as follows: a distribution is maintained
on a certain set, and at each step the probability assigned to i is multi
plied or divided by (1 + C(i)) where C(i) is some kind of "payoff" for
element i. (Rescaling may be needed to ensure that the new values form
a distribution.) Some examples include: the Ada Boost algorithm in ma
chine learning [FS97]; algorithms for game playing studied in economics
(see below), the PlotkinShmoysTardos algorithm for packing and covering
