The Value of Human Expertise
TL;DR
This work proposes an approach to evaluating policies that provides tighter performance guarantees if the decision maker's belief happens to be correct, and shows that if computing a policy's worst-case performance is a convex program, then the value of human expertise is equal to the minimax gap of a max-min problem.
Abstract
We consider optimization applications with unknown parameters where the decision maker believes that the optimal value of the nominal problem-the optimization problem they would have solved if the true parameters were known-is unlikely to be large. This belief derives from information that humans have that is not captured in datasets, obtained from domain knowledge and interacting with the physical world. We propose an approach to evaluating policies that provides tighter performance guarantees if the decision maker's belief happens to be correct. Our main result shows that if computing a policy's worst-case performance is a convex program, then the value of human expertise-the maximum improvement in performance guarantees that can be obtained from the belief about the nominal problem-is equal to the minimax gap of a max-min problem. We illustrate our developments in assortment optimization and shortest path problems.