Learning to Solve Optimization Problems with Hidden Components: Applications in Automated Treatment Planning

Designing optimization models that capture decision-maker preferences typically requires guidance from domain experts. We can instead employ machine learning (ML) to design contextual optimization models using data sets of past decisions. In this thesis, we propose techniques to formulate and solve problems where the objective or the feasible set is dependent on decision-maker preferences. We apply these methods to automate the design of personalized radiation therapy treatments for head-and-neck cancer patients. Here, the prevailing framework is Knowledge-based planning (KBP), which is a two-stage pipeline that involves generating an expected dose and optimizing a treatment to deliver the generated dose. We first propose an ensemble learning framework for Inverse Linear Optimization (ILO), which is a structured prediction problem for estimating the cost vector of a linear program from observed decisions. Our framework specializes to existing variants in the literature, admits new solution algorithms, and includes a statistical goodness-of-fit metric. We employ our framework to develop the first ensemble KBP pipeline that incorporates multiple different dose generation models to yield better treatments than existing single-dose pipelines. Next, we develop a deep learning-based dose generation model that uses a generative adversarial network to map from CT images to dose distributions. Previous dose generation models employed classical ML to estimate dose summary statistics. Our approach outperforms classical models on clinical metrics. We then explore contextual optimization when the feasible set varies as a function of features. We present Interior Point Methods with Adversarial Networks (IPMAN), an algorithm for learning the feasible set and predicting corresponding optimal decisions for contextual problems. We prove our approach yields optimality guarantees and generalization bounds. We then re-cast dose generation as an optimization problem and implement IPMAN to predict optimal doses. Our predictions achieve clinical metrics better than baselines and also demonstrate a transfer learning to new clinics that use different metrics. Finally, motivated by data augmentation for IPMAN, we consider the task of sampling infeasible decisions from an optimization problem. We present a Markov Chain Monte Carlo algorithm for sampling from the complement of a polyhedron that provably covers the complement and demonstrate its effectiveness in numerical experiments.

Department dc:contributor.department

Mechanical and Industrial Engineering

Year dc:date.issued

2020

Author dc:creator

• Mahmood, Rafid

Advisor dc:contributor.advisor

• Chan, Timothy C Y

• constrained optimization
• machine learning
• medical decision-making
• radiation therapy

Statement dc:rights

• Attribution 4.0 International

Licence dc:rights.uri

• http://creativecommons.org/licenses/by/4.0/

Handle dc:identifier.uri

http://hdl.handle.net/1807/103339

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/103339