Title: A Robust Utility Learning Framework via Inverse Optimization,
Abstract: 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 non-cooperative 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 as well as to data
from a social game experiment designed to encourage energy efficient behavior
amongst 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.