4,528 research outputs found
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 + 1 samples of
the black-box function per iteration of the algorithm, where 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 at
low temperatures. The Hall conductance is unaffected by the Rashba coupling.Comment: 4 pages, 4 figure
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