Online Optimization of Product-Form Networks

TL;DR

This paper introduces an online gradient algorithm for optimizing product-form networks by using empirical frequency measurements, reducing computational costs and adapting to dynamic environments while ensuring convergence despite noisy estimates.

Contribution

It presents a novel online gradient method that leverages empirical data to optimize product-form networks efficiently and adaptively.

Findings

Reduces computational burden compared to traditional gradient calculations.

Ensures convergence to a global optimum despite noisy, biased estimates.

Adapts naturally to slow environmental changes in dynamic settings.

Abstract

We develop an online gradient algorithm for optimizing the performance of product-form networks through online adjustment of control parameters. The use of standard algorithms for finding optimal parameter settings is hampered by the prohibitive computational burden of calculating the gradient in terms of the stationary probabilities. The proposed approach instead relies on measuring empirical frequencies of the various states through simulation or online operation so as to obtain estimates for the gradient. Besides the reduction in computational effort, a further benefit of the online operation lies in the natural adaptation to slow variations in ambient parameters as commonly occurring in dynamic environments. On the downside, the measurements result in inherently noisy and biased estimates. We exploit mixing time results in order to overcome the impact of the bias and establish sufficient conditions for convergence to a globally optimal solution.