Inverse optimization seeks the hidden objective that explains observed decisions, yet existing methods typically recover a single objective and ignore uncertainty in the underlying preferences. We develop a Bayesian framework that represents the unknown objective by a posterior distribution, combining a boundedrationality choice model with prior information to quantify uncertainty directly. We establish geometric conditions for identifiability, prove posterior consistency, derive the optimal n−1/2, contraction rate, obtain a Bernstein–von Mises approximation, and present a finite-sample concentration bound together with a robust fractional posterior for misspecified behavioural models. Posterior inference is performed using gradient-based Markov chain Monte Carlo and a Laplace approximation. Simulation studies demonstrate accurate recovery under noisy, misspecified, nonlinear, and high-dimensional settings, while a controlled clinical example illustrates uncertainty quantification in hidden decision preferences. The proposed framework extends inverse optimization from point estimation to statistically principled uncertainty quantification, providing a rigorous foundation for learning decision objectives from imperfect observations.
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Bayesian Inverse Optimisation under Uncertainty Posterior Inference for Hidden Decision Objectives
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Received: 02 Aug 2026 | Revised: 19 Sep 2026 | Accepted: 09 Oct 2026 | Published: 16 Oct 2026
Abstract
Keywords
inverse optimization | Bayesian inference | uncertainty quantification | bounded rationality | posterior consistency | Markov chain Monte-Carlo
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