Protocols for Stochastic Shortest Path Problems with Dynamic Learning by Vural Aksakalli

The research problem considered in this dissertation, in its most broad setting, is a stochastic shortest path problem in the presence of a dynamic learning capability (SDL). Specifically, a spatial arrangement of possible-obstacles needs to be traversed as swiftly as possible, and the status of the obstacles may be disambiguated (at a cost) en route. No efficiently computable optimal protocol is known and many similar problems have been proven intractable. Chapter 1 defines SDL in continuous and discrete settings, and introduces the Random Disambiguation Paths Problem (RDP), a continuous variant of SDL wherein a decision maker (DM) needs to swiftly navigate from one given location to another through an arrangement of disc-shaped possible-obstacles in the plane. At the outset, the DM is given the respective probabilities that the discs are truly obstacles and, en route, when situated on a disc’s boundary, the DM has the option to disambiguate the disc, i.e., learn at a cost if the disc is truly an obstacle. The central question is to find a protocol that decides what and where to disambiguate en route so as to minimize the expected length of the traversal. For any RDP instance, the continuous plane can be approximated by a graph (a lattice), and edges that intersect discs can be appropriately probabilistic, giving rise to the Discrete RDP Problem (DRDP), which is a special case of the well-known Canadian Traveler Problem (CTP) in the literature, but with statistical dependency among the edges. The chapter concludes with a comprehensive review of the litera-