High Dimensional Decision Making, Upper and Lower Bounds

Abstract

A decision maker's utility depends on her action $a\in A\subset {\mathbb{R}}^d$ and the payoff relevant state of the world $\theta \in \Theta$. One can define the value of acquiring new information as the difference between the maximum expected utility pre- and post information acquisition. In this paper, I find asymptotic results on the expected value of information as $d\to \infty$, by using tools from the theory of (sub)-Guassian processes and generic chaining.