Advances in Data-Driven Decision-Making: A Mathematical Optimization Perspective

Data-driven decision-making holds great potential for increasing the productivity of companies and organizations. However, this potential is not yet fully leveraged as there are still certain barriers to implementing such systems in practice. This doctoral thesis presents three research papers following the same purpose: offering solution approaches for common challenges in the field of data-driven decision-making via novel optimization procedures. The three challenges under consideration are the (i) explainability, (ii) scalability, and (iii) accessibility of data-driven decision-making approaches. Besides individual contributions in the respective area of application, each paper targets one of the three challenges in particular. The first paper of this doctoral thesis develops an explainable data-driven algorithm for personalized medicine. In particular for off-policy learning, where the goal is to derive personalized treatment decisions based on individual patient characteristics from observational data, e.g., randomized control trials. The resulting treatment decisions can be presented in disjunctive normal form, i.e., OR-of-ANDs, and fulfill explainability demands from clinical practice. This is shown in a user study, in which we ask actual clinical practitioners to rate the interpretability of our approach. The main contribution, that makes this new algorithm possible, lies in the field of mathematical optimization. That is, a novel formulation of off-policy learning as a mixed-integer linear program, and a tailored column generation procedure within a branch-and-bound framework to solve it. The second paper proposes an efficient Monte Carlo tree search (MCTS) for data-driven dynamic police patrolling. Thereby, the goal is to optimize and dynamically adjust patrol routes of police units through their patrol beats, i.e., predefined patrol areas, with the aim of crime risk reduction. In contrast to state-of-the-art patrol algorithms based on vehicle routing problem formulations, the novel MCTS approach scales to real-world problem instances. This is confirmed in a simulation study using actual crime and operational data from Chicago. Again, the main driving force behind the new approach is a novel problem formulation as a Markov decision process. The latter allows to efficiently guide the optimization process within MCTS by tailored roll-out policies. The third paper is a theoretical contribution to the field of neural learning. Neural networks have shown the potential to create immense value in the area of data-driven decision-making. However, their training usually relies on expert knowledge gained over years. The contribution of this work is to develop a novel optimization approach for learning parameters of neural networks, that allows for general convergence guarantees and refrains from any hyperparameters related to training. Thus, the tuning of hyperparameters, which are only difficult to assess, and the manual inspection of convergence by examining loss curves becomes obsolete. The proposed algorithm is a first step towards turning the training of neural networks into a fully automated process and, thus, making neural networks more accessible to non-experts. This thesis provides solution approaches for three major challenges in data-driven decision-making. The presented results are mainly theoretical contributions and, thus, are likely to generalize to different areas of application