Robust Decision Making using a General Utility Set

Elicitation of an exact utility function of a decision maker is challenging. In this paper, we address the problem of ambiguity and inconsistency in utility assessments by studying a robust utility-based decision making model where the utility function belongs to a set of general increasing utility functions. We build a robust framework in which the utility function belongs to a set. This set on the utility function is described by boundary and auxiliary conditions. We consider a maximin problem that maximizes the worst-case expected utility of random outcome over the set, thereby hedging the risk arising from uncertainty of the utility function. We study the implications of the uncertain utility on the objective function value of this robust decision model and show that under suitable conditions the Sample Average Approximation (SAA) of a Lagrangian function associated with this model can be solved using a mixed integer linear program. We show that the optimum objective value of the SAA converges to its true counterpart at an exponential rate and we harness this convergence property to present a heuristic which provides a feasible solution for the SAA problem. We illustrate model properties using a portfolio investment problem where investment gains and losses are valued using different uncertain decision (dis)utilities. We also provide computational insights by solving the SAA of this problem as a mixed integer linear program and using our heuristic.