Constraint Inference using Quality-based Robust-inverse Optimization for Radiation Therapy

Abstract

Traditional radiation therapy treatment planning involves manual, iterative adjustments to optimization model parameters, often guided by the oncologist’s judgment. This process can introduce implicit constraints that may not be obvious to treatment planners. One approach to infer the parameters of a problem from observed solutions is inverse optimization, which has been extensively studied in the context of radiation therapy planning. While traditional forward optimization relies on predefined problem parameters to find an optimal solution, inverse optimization seeks to determine these parameters based on one or multiple observations that may be optimal, feasible, or infeasible. When dealing with uncertain or noisy data, robust optimization can be employed to address uncertainty. Similarly, extensive research has been conducted on the application of robust optimization techniques to radiation therapy planning.

This thesis introduces an inverse optimization approach that infers the complete constraint matrix of a linear forward optimization problem while considering multiple uncertain feasible observations. We discuss application-specific considerations for applying inverse optimization to radiation therapy treatment plans and present a formulation that adapts to uncertainty using a polyhedral uncertainty set. We propose an iterative single-constraint inference algorithm that demonstrates superior performance in terms of computational efficiency and the quality of inferred constraints compared to existing methods in the literature. The proposed algorithm is then evaluated on a dataset of prostate cancer treatment plans, showcasing its practical applicability in medical treatment planning. By leveraging the results from this algorithm, we aim to streamline the development of radiation therapy treatment plans by providing guidelines that better reflect the oncologist’s preferences, reducing the number of required iterations and conserving valuable resources such as time and cost.