# Inverse Optimization and Inference models

### UTILITY INFERENCE UNDER UNCERTAINTY

Given an optimal or near-optimal solution, an inverse optimization problem determines objective function parameters of the forward optimization problem such that the solution becomes optimal for the forward problem. However, there is often uncertainty in the observed solutions and hence there is a need to develop robust inverse optimization models.

### A COMBINED INVERSE OPTIMIZATION FOR PERSONALIZED DIET

Many patients who suffer from hypertension or diabetes have to change their diet and lifestyle to control their symptoms and the progress of their illness. However, the diets recommended often follow a one-size-fits-all philosophy and are rarely adjusted to the patients’ taste and preferences. Hence, many patients find it hard to adhere to such diets. We use inverse optimization to find a personalized diet based on a patient’s previous choices.

### DATA-DRIVEN INVERSE OPTIMIZATION TO PERSONALIZED CANCER CARE

The medical decisions of experts, for instance the radiation treatment plan approved by oncologists, can be observed. However, the true underlying criteria based on which they approved or rejected a plan is not known. We develop data-driven inverse optimization models to infer the constraints parameters of an optimization problem to understand such expert-driven decisions better.

### Inverse Learning: A Data-driven Framework to Recover Linear Optimizations

Inverse optimization is an area of study where the purpose is to infer the unknown parameters of an optimization problem when a set of observations is available on the previous decisions made in the settings of the problem. We develop a framework to effectively and efficiently infer the cost vector of a linear optimization problem based on multiple observations on the decisions made previously.