Planning in partially observable domains is a notoriously difficult problem. However, in many real-world scenarios, planning can be simplified by decomposing the task into a hierarchy of smaller planning problems which, can then be solved independently of one another. Several approaches, mainly dealing with fully observable domains, have been proposed to optimize a plan that decomposes according to a hierarchy specified a priori. Some researchers have also proposed to discover hierarchies in fully observable domains. In this thesis, we investigate the problem of automatically discovering planning hierarchies in partially observable domains. The main advantage of discovering hierarchies is that, for a plan of a fixed size, hierarchical plans can be more expressive than non-hierarchical ones. Our solution frames the discovery and optimization of a hierarchical policy as a non-convex optimization problem. By encoding the hierarchical structure as variables of the optimization problem, we can automatically discover a hierarchy. Successfully solving the optimization problem therefore yields an optimal hierarchy and an optimal policy. We describe several techniques to solve the optimization problem. Namely, we provide results using general non-linear solvers, mixed-integer linear and non-linear solvers or a form of bounded hierarchical policy iteration. Our method is flexible enough to allow any parts of the hierarchy to be specified based on prior knowledge while letting the optimization discover the unknown parts. It can also discover hierarchical policies, including recursive policies, that are more compact (potentially infinitely fewer parameters).

Planning in partially observable domains is a notoriously difficult problem. However, in many real-world scenarios, planning can be simplified by decomposing the task into a hierarchy of smaller planning problems which, can then be solved independently of one another. Several approaches, mainly dealing with fully observable domains, have been proposed to optimize a plan that decomposes according to a hierarchy specified a priori. Some researchers have also proposed to discover hierarchies in fully observable domains. In this thesis, we investigate the problem of automatically discovering planning hierarchies in partially observable domains. The main advantage of discovering hierarchies is that, for a plan of a fixed size, hierarchical plans can be more expressive than non-hierarchical ones. Our solution frames the discovery and optimization of a hierarchical policy as a non-convex optimization problem. By encoding the hierarchical structure as variables of the optimization problem, we can automatically discover a hierarchy. Successfully solving the optimization problem therefore yields an optimal hierarchy and an optimal policy. We describe several techniques to solve the optimization problem. Namely, we provide results using general non-linear solvers, mixed-integer linear and non-linear solvers or a form of bounded hierarchical policy iteration. Our method is flexible enough to allow any parts of the hierarchy to be specified based on prior knowledge while letting the optimization discover the unknown parts. It can also discover hierarchical policies, including recursive policies, that are more compact (potentially infinitely fewer parameters).