Online Optimization of Product-Form Networks and Rydberg Gases
Jaron Sanders, KTH
12-1pm 21st Oct 2016
AbstractWe start this talk by discussing a gradient algorithm that optimizes 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. The algorithm can be applied in a wide variety of systems, including queueing networks, loss networks, and wireless networks.
The algorithm is so versatile that we can even apply it to complex physical systems. We will end the talk by introducing you to a relationship that exists between the dynamics of ultracold Rydberg gases (a quantummechanical system studied for its applications in quantum computing), and a stochastic process that models certain wireless random-access networks. We then transfer the optimization algorithm that we have discussed to the realm of Rydberg gases, and see how it can determine laser intensities such that particles in the Rydberg gas are excited with specified target excitation probabilities. This provides physicists control over mixed-state populations, which can in the future be of interest to mixed-state quantum computing.
IEEE TAC 61 (7), p. 1838 - 1853, July 2016, Online Network Optimization Using Product-Form Markov Processes'
Phys. Rev. Lett. 112, 163001, April 2014, Wireless Network Control of Interacting Rydberg Atoms'