Using Importance Samping in Estimating Weak Derivative

In this paper we study simulation-based methods for estimating gradients in stochastic networks. We derive a new method of calculating weak derivative estimator using importance sampling transform, and our method has less computational cost than the classical method. In the context of M/M/1 queueing network and stochastic activity network, we analytically show that our new method won't result in a great increase of sample variance of the estimators. Our numerical experiments show that under same simulation time, the new method can yield a narrower confidence interval of the true gradient than the classical one, suggesting that the new method is more competitive

Quantile Optimization via Multiple Timescale Local Search for Black-box Functions

We consider quantile optimization of black-box functions that are estimated with noise. We propose two new iterative three-timescale local search algorithms. The first algorithm uses an appropriately modified finite-difference-based gradient estimator that requires $2d$ + 1 samples of the black-box function per iteration of the algorithm, where $d$ is the number of decision variables (dimension of the input vector). For higher-dimensional problems, this algorithm may not be practical if the black-box function estimates are expensive. The second algorithm employs a simultaneous-perturbation-based gradient estimator that uses only three samples for each iteration regardless of problem dimension. Under appropriate conditions, we show the almost sure convergence of both algorithms. In addition, for the class of strongly convex functions, we further establish their (finite-time) convergence rate through a novel fixed-point argument. Simulation experiments indicate that the algorithms work well on a variety of test problems and compare well with recently proposed alternative methods

Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with Rashba Interaction in a Perpendicular Magnetic Field

We study transport properties of a two-dimensional electron system with Rashba spin-orbit coupling in a perpendicular magnetic field. The spin orbit coupling competes with Zeeman splitting to introduce additional degeneracies between different Landau levels at certain magnetic fields. This degeneracy, if occuring at the Fermi level, gives rise to a resonant spin Hall conductance, whose height is divergent as 1/T and whose weight is divergent as $-\ln T$ at low temperatures. The Hall conductance is unaffected by the Rashba coupling.Comment: 4 pages, 4 figure