Optimal decision making in the face of uncertainty is an active area of research in artificial intelligence. In this thesis, I present the sport of curling as a novel application domain for research in optimal decision making. I focus on one aspect of the sport, the hammer shot, the last shot taken before a score is given, and how selecting this shot can be modelled as a low-dimensional optimization problem with a continuous action space and stochastic transitions. I explore the unique research challenges that are brought forth when optimizing in a setting where there is uncertainty in the action outcomes. I then survey several existing optimization strategies and describe a new optimization algorithm called Delaunay Sampling, adapted from a method based on Delaunay triangulation. I compare the performance of Delaunay Sampling with the other algorithms using our curling physics simulator and show that it outperforms these other algorithms. I also show that, with a few caveats, Delaunay Sampling exceeds the performance of Olympic-level humans when selecting strategies for hammer shots.
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