University of Montreal
Faculty of Arts and Sciences Department of Computer Science and Operations Research |
Felisa J. Vázquez-Abad, Associate Professor
Sensitivity Analysis:
Estimation of gradients of stationary averages is a difficult and important
problem both for on-line as well as off-line optimization. The Phantom
RPA method was introduced in [9], as a generalization of the phantom
finite difference of my PhD Thesis. This paper has been cited recently
by many other researchers in the Discrete Event Systems area, and has had
an impact in the development of sensitivity estimators. Further generalizations
of this method appear in [3], [12] and [70], and novel applications are
in [2] and [67].
Surrogate Estimation:
The short paper [20] summarizes the results in Vázquez-Abad
and Kushner, ``A surrogate estimation approach for adaptive routing
in communication networks'', Brown University Report LCDS/CCS, No.
1990-2. It proposes a method akin to the indirect estimation of Glynn and
Whitt, but here one uses the information on the sensitivities w.r.t. some
variables in order to approximate sensitivities w.r.t. the desired controls.
Estimating global sensitivities via local ones is crucial in decentralization
and distribution of the control for large complex systems, as our examples
in [20] show, where in addition to decentralizing the control structure,
a dramatic reduction in computational effort is achieved with this method.
Generalizations of this approach are in [69].
Functional Estimation:
We have extended the idea behind the phantom method, to create a method
for functional estimation in [6], extending the results of [19].
We call this new method the Split-and-Merge Simulation Tree. In
[15] and [66] we present the implementation of the method to an age replacement
policy problem, with new results for the problem and a theoretical analysis
of the algorithmic efficiency modeling
the simulation tree as a branching process.
Simulation Methods:
Evaluation of certain important quantities in Risk Theory has attracted
the attention of mathematicians and practitioners for decades. It is only
lately that simulation has been accepted as a numerical method for approximating
such quantities. In [2] I have proposed a new method for estimating
the probability of ruin of an insurance company using Importance Sampling
(IS). In the same work, we develop the sensitivity estimators for three
simulation methods: IS and two other previously known methods. Two of them
are non-trivial applications of the RPA method. In [11] we propose a change of
measure approach for the evaluation of Asian Options. In addition to estimating rare
events (when the option is out of the money) through a change of measure, we
accelerate convergence using stochastic approximation to seek the best change of
measure.