Constraint-based optimization and utility elicitation using the minimax decision criterion

In many situations, a set of hard constraints encodes the feasible configurations of some system or product over which multiple users have distinct preferences. However, making suitable decisions requires that the preferences of a specific user for different configurations be articulated or elicited, something generally acknowledged to be onerous. We address two problems associated with preference elicitation: computing a best feasible solution when the user's utilities are imprecisely specified; and developing useful elicitation procedures that reduce utility uncertainty, with minimal user interaction, to a point where (approximately) optimal decisions can be made. Our main contributions are threefold. First, we propose the use of minimax regret as a suitable decision criterion for decision making in the presence of such utility function uncertainty. Second, we devise several different procedures, all relying on mixed integer linear programs, that can be used to compute minimax regret and regret-optimizing solutions effectively. In particular, our methods exploit generalized additive structure in a user's utility function to ensure tractable computation. Third, we propose various elicitation methods that can be used to refine utility uncertainty in such a way as to quickly (i.e., with as few questions as possible) reduce minimax regret. Empirical study suggests that several of these methods are quite successful in minimizing the number of user queries, while remaining computationally practical so as to admit real-time user interaction.