International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

MARKOV DECISION PROCESS MODELS FOR IMPROVING EQUITY IN LIVER ALLOCATION

In the United States, end-stage liver disease (ESLD) patients are prioritized primarily by their Model for End-stage Liver Disease score (MELD) to receive organ offers. Therefore, patients are required to update their MELD score at predefined frequencies that depend on the patient's last reported score. One aim of this dissertation is to mitigate inequities that stem from patients' flexibility regarding MELD score updates. We develop a Markov decision process (MDP) model to examine the degree to which an individual patient can benefit from the updating flexibility, and provide a menu of updating requirements that balance inequity and data processing more efficiently than the current updating requirements. We also derive sufficient conditions under which a structured optimal updating policy exists. As the coordinator of the harvesting Organ Procurement Organization (OPO) extends offers according to MELD score prioritization, the organ becomes less desirable. To avoid not placing the organ, the OPO coordinator can initiate an expedited placement, i.e., offer the organ to a transplant center, which can then allocate it to any of its patients. A second aim of this dissertation is to mitigate inequities induced by the OPO coordinator's premature departure from the prioritized list of patients via an expedited placement. As a preliminary step to studying the inequity induced by expedited liver placement, we conduct an extensive analysis of the current expedited liver placement practice based on recent data. We investigate different aspects of extending offers, e.g., the number of offers extended concurrently, and patients' response characteristics. Several of the results from this analysis serve as inputs for a second MDP model that examines how many concurrent offers the OPO coordinator should extend and when the coordinator should initiate an expedited placement. Numerical experimentation reveals a structured optimal policy, and we test the sensitivity of the model outcomes with respect to changes in model inputs. Lastly, we examine how our model outputs compare to the analogous measures observed in current practice and how they can be used to improve current practice

Doubly-Asynchronous Value Iteration: Making Value Iteration Asynchronous in Actions

Value iteration (VI) is a foundational dynamic programming method, important for learning and planning in optimal control and reinforcement learning. VI proceeds in batches, where the update to the value of each state must be completed before the next batch of updates can begin. Completing a single batch is prohibitively expensive if the state space is large, rendering VI impractical for many applications. Asynchronous VI helps to address the large state space problem by updating one state at a time, in-place and in an arbitrary order. However, Asynchronous VI still requires a maximization over the entire action space, making it impractical for domains with large action space. To address this issue, we propose doubly-asynchronous value iteration (DAVI), a new algorithm that generalizes the idea of asynchrony from states to states and actions. More concretely, DAVI maximizes over a sampled subset of actions that can be of any user-defined size. This simple approach of using sampling to reduce computation maintains similarly appealing theoretical properties to VI without the need to wait for a full sweep through the entire action space in each update. In this paper, we show DAVI converges to the optimal value function with probability one, converges at a near-geometric rate with probability 1-delta, and returns a near-optimal policy in computation time that nearly matches a previously established bound for VI. We also empirically demonstrate DAVI's effectiveness in several experiments