Online Optimization of Product-Form Networks and Rydberg Gases

Abstract

We 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.

Source material:

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'

Short Bio

Jaron Sanders was born in Eindhoven, The Netherlands, on November 6, 1987. After his Bachelor degree in Applied Physics and Master degrees in Applied Physics and Applied Mathematics, he started his PhD studies under the supervision of Johan van Leeuwaarden and Sem Borst at the Eindhoven University of Technology. Jaron's PhD research focussed on the critical scaling of service systems, the optimal control of stochastic systems, and probabilistic modeling of Rydberg gases. After his defense Jaron started as a post-doctoral researcher at the Royal Institute of Technology in Stockholm, Sweden. He now works on training of neural networks, and online clustering techniques with Alexandre Proutière.

Venue

Large Conference Room, O'Reilly Institute