Stochastic Gradient Estimation Using a Single
Design Point
Jamie R Wieland and Bruce W Schmeiser (Purdue
University)
Abstract:
Using concepts arising in control variates, we propose
estimating gradients using Monte Carlo data from a single design point. Our
goal is to create a statistically efficient estimator that is easy to
implement, with no analysis within the simulation oracle and no unknown
algorithm parameters. We compare a simple version of the proposed method to
finite differences and simultaneous perturbation, assuming first and
second-order linear logic models and response surfaces. Results of the
analysis indicate that the proposed gradient estimator is unbiased with
variance that is inversely related to the variance of the assumed input model.
Compared to the only existing single design-point method, the proposed
gradient estimator is advantageous in that its variance is not dependent on
the magnitude of the response surface at the design point of interest and also
decreases as the simulation run length increases.
Efficient Simulation of Population Overflow in
Parallel Queues
Victor F. Nicola and Tatiana S. Zaburnenko
(University of Twente)
Abstract:
In this paper we propose a state-dependent importance
sampling heuristic to estimate the probability of population overflow in
networks of parallel queues. This heuristic approximates the "optimal"
state-dependent change of measure without the need for difficult mathematical
analysis or costly optimization involved in adaptive methodologies.
Comprehensive simulations of networks with an arbitrary number of parallel
queues and different traffic intensities yield asymptotically efficient
estimates (with relative error increasing sub-linearly in the overflow level)
where no other state-independent importance sampling techniques are known to
be efficient. The efficiency of the proposed heuristic surpasses those based
on adaptive importance sampling algorithms, yet it is easier to determine and
implement and scales better for large networks.
The Impact of Ordinal on Response Surface
Methodology
Sara Jian Oon (Princeton University) and Loo Hay Lee
(National University of Singapore)
Abstract:
Traditionally, Response Surface Methodology (RSM) is
cardinal in nature. Ordinal optimization was only introduced recently. Since
ordinal optimization has been proven to be successful in certain applications,
this paper aims to investigate whether ordinal optimization improves RSM by
developing ordinal RSM and comparing it with cardinal RSM in terms of
efficiency, accuracy and consistency. Assuming that the performances of
systems can be expressed as functions of their parameters, both ordinal and
cardinal RSM are simulated for several simple multivariable mathematical
functions and the effectiveness of ordinal RSM evaluated. It was found that
ordinal does not always improve RSM, especially in functions which exhibit a
large gradient change over a small region.
