High Dimensional Decision Making, Upper and Lower Bounds
This work addresses theoretical limits in decision theory for high-dimensional settings, providing foundational insights for researchers in economics and machine learning.
The paper tackles the problem of quantifying the value of information in high-dimensional decision-making by deriving asymptotic bounds on the expected value of information as dimensionality increases, using tools from Gaussian processes and generic chaining.
A decision maker's utility depends on her action $a\in A \subset \mathbb{R}^d$ and the payoff relevant state of the world $θ\in Θ$. 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.