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This paper explores optimization scenarios with unknown parameters, focusing on the value of human expertise that informs decision-making beyond available datasets. By leveraging human insights, the authors propose a method for policy evaluation that tightens performance guarantees when the decision maker's beliefs about optimal values are accurate. The key finding reveals that in cases where worst-case performance is a convex program, the value of human expertise corresponds to the minimax gap of a max-min problem, with applications demonstrated in assortment optimization and shortest path problems.
Human expertise can significantly enhance performance guarantees in optimization, aligning with the minimax gap of decision-making problems.
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.
