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Conventional inverse optimization inputs a solution and finds the parametersof an optimization model that render a given solution optimal. The literaturemostly focuses on inferring the objective function in linear problems whenaccepted solutions are provided as input. In this paper, we propose an inverseoptimization model that inputs several accepted and rejected solutions andrecovers the underlying convex optimization model that can be used to generatesuch solutions. The novelty of our model is two-fold: First, we focus oninferring the parameters of the underlying convex feasible region. Second, theproposed model learns the convex constraint set from a set of past observationsthat are either accepted or rejected by an expert. The resulting inverse modelis a mixed-integer nonlinear problem that is complex to solve. To mitigate theinverse problem complexity, we employ variational inequalities and thetheoretical properties of the solutions to derive a reduced formulation thatretains the complexity of its forward counterpart. Using realistic breastcancer patient data, we demonstrate that our inverse model can utilize a subsetof past accepted and rejected treatment plans to infer clinical criteria thatcan lead to nearly guaranteed acceptable treatment plans for future patients.

Expert-Guided Inverse Optimization for Convex Constraint Inference