# A Robust Utility Learning Framework via Inverse Optimization

## TL;DR

This paper introduces a robust utility learning framework using inverse optimization, incorporating heteroskedastic inference and ensemble methods to model heterogeneous user preferences in smart infrastructure applications.

## Contribution

It presents a novel correlated utility learning approach that estimates noise covariance and leverages ensemble techniques for improved forecasting in heterogeneous user settings.

## Key findings

- Effective utility estimation in a toy Bertrand-Nash game
- Successful application to social energy efficiency experiments
- Enhanced forecasting accuracy with ensemble methods

## 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.