High Dimensional Decision Making, Upper and Lower Bounds

TL;DR

This paper investigates the asymptotic behavior of the value of information in high-dimensional decision-making scenarios, using advanced probabilistic tools to analyze the limits as the dimension grows large.

Contribution

It provides new asymptotic results on the expected value of information in high-dimensional settings, extending decision theory with probabilistic methods.

Findings

Expected value of information converges or behaves predictably as dimension increases.

Utilizes Gaussian process theory and generic chaining for analysis.

Offers insights into decision-making in high-dimensional environments.

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.