Groupe d’études et de recherche en analyse des décisions

Ersatz estimation: gradient relationships for complex systems under uncertainty

Felisa Josefina Vazquez-Abad Hunter College (CUNY), États-Unis

Many optimisation techniques rely on gradients or sensitivity information to better tune the control variables towards optimality. Under uncertainty, it is often the case that a closed expression for the gradient is unavailable. I this situation, gradient estimators must be used instead, but these are typically very costly.

This talk presents a methodology for finding relationships between gradients with respect to the different parameters of the model and discusses how these can be used to synthesise scalable calculations in complex systems. In the 1990's, several researchers independently proposed ad-hoc transformations of the derivatives to simplify the problem. Since that time, I have tried to formulate a general methodology to justify such transformations, which allow us to express the derivatives with respect to the control variables of interest in terms of simpler derivatives, obtained with respect to other parameters in the model. An "ersatz" derivative is the estimator obtained via the inverse transformations. My approach uses basic methods in Physics, such as time scale changes and changes of variables, or of reference framework.

I will provide examples of application to an insurance portfolio, a telecommunications network and a transportation system, to discuss the significance of the results, and I will attempt to give a general idea of an on-going research effort, rather than to present a finished Theory of gradient estimation.