A Robust Utility Learning Framework via Inverse Optimization

In many smart infrastructure applications, flexibility in achieving sustainability goals can be gained by engaging end users. However, these users often have heterogeneous preferences that are unknown to the decision maker tasked with improving operational efficiency. Modeling user interaction as a continuous game between noncooperative players, we propose a robust parametric utility learning framework that employs constrained feasible generalized least squares estimation with heteroskedastic inference. To improve forecasting performance, we extend the robust utility learning scheme by employing bootstrapping with bagging, bumping, and gradient boosting ensemble methods. Moreover, we estimate the noise covariance, which provides approximated correlations between players, which we leverage to develop a novel correlated utility learning framework. We apply the proposed methods both to a toy example arising from Bertrand–Nash competition between two firms and to data from a social game experiment designed to encourage energy efficient behavior among smart building occupants. Using occupant voting data for shared resources such as lighting, we simulate the game defined by the estimated utility functions to demonstrate the performance of the proposed methods.