The optimizer's curse and how to beat it

Abstract

Optimization decisions often rely on estimated expected value, which faces the hurdle of the optimizer’s curse: the propensity to overestimate the expected value due to optimistic bias. This is especially prevalent where there are many choices, leading to disappointment as outcomes are usually worse than predicted. To address this bias, it’s advised to utilize Bayesian methods that account for the uncertainty in value estimates. This involves setting a prior distribution on the possible values, and after conducting decision analysis, Bayes’ rule is applied to compute the posterior distribution given the observed value estimates. Thus, the selection of alternatives is done based on the posterior means, and not the estimated values. This approach not only accounts for the uncertainty in value estimates but also adjusts for the bias implicit in the optimization process by lowering high estimated values. Therefore, skepticism is justified when considering options with the highest expected value, and the use of Bayes’ Theorem is recommended to better handle decision analysis uncertainties. – AI-generated abstract.