The expected value of perfect information in the optimal evolution of stochastic systems

Abstract

Methodological research into optimization problems and techniques has a long history in the System and Decision Sciences Program at IIASA. Most recently, effort -- of which this paper forms a part -- has concentrated on the analysis of stochastic systems. For a very general model of a stochastic optimization problem with an infinite planning horizon of discrete time, the author analyzes the stochastic process describing the marginal expected value of perfect information (EVPI) about the future of the system. He demonstrates two intuitively obvious properties of this marginal EVPI process: that its values are completely predictable at each actual decision point and that its expected values tend to decline over the future since information is potentially worth more the sooner it is available. The author is currently working on continuous time analogs of these results, which are unfortunately fraught with technical difficulties. This work should be viewed as a theoretical prolegomenon to computational studies aimed at estimating the value of perfect or partial information in the control of stochastic systems. The central observation here is that the extra complexity and computational burden of introducing random parameters into planning or control models may sometimes be unnecessary. The (marginal) EVPI at decision points is the natural measure by which their modeling efficacy can be evaluated.