In the *Cross Entropy Method*, we wish to estimate the likelihood

Here is a random variable whose distribution is known and belongs to a parametrized family of densities . Further is often a solution to an optimization problem.

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# Category: Optimization

## Cross Entropy Method

## Online Convex Optimization

## Gradient Descent

## A Network Decomposition

## Congestion Control

## Gale-Eisenberg Market

In the *Cross Entropy Method*, we wish to estimate the likelihood

Here is a random variable whose distribution is known and belongs to a parametrized family of densities . Further is often a solution to an optimization problem.

We consider the setting of sequentially optimizing the average of a sequence of functions, so called *online convex optimization*.

We consider one of the simplest iterative procedures for solving the (unconstrainted) optimization

We consider a decomposition of the following network utility optimization problem

SYS:

We argue, in a slightly informal manner, that queueing networks implicitly optimize a utility function subject to constraints on network capacity. We start with the simple example of a closed queueing network and, as we shall discuss, a motivating example is the Transmission Control Protocol which controls the number of packets in transfer on an Internet connection.

The Gale-Eisenberg is a nice example were the distributed decisions of buyers and sellers have an equilibrium which solves an optimization problem.