  Inverse optimization has been increasingly used to estimate unknown
parameters in an optimization model based on decision data. We show that such a
point estimation is insufficient in a prescriptive setting where the estimated
parameters are used to prescribe new decisions. The prescribed decisions may be
low-quality and misaligned with human intuition and thus are unlikely to be
adopted. To tackle this challenge, we propose conformal inverse optimization,
which seeks to learn an uncertainty set for the unknown parameters and then
solve a robust optimization model to prescribe new decisions. Under mild
assumptions, we show that our method enjoys provable guarantees on solution
quality, as evaluated using both the ground-truth parameters and the decision
maker's perception of the unknown parameters. Our method demonstrates strong
empirical performance compared to classic inverse optimization.
