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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).

The need to analyze and closely study the gene related mechanisms motivated the research on the modeling and control of gene regulatory networks (GRN). Dierent approaches exist to model GRNs / they are mostly simulated as mathematical models that represent relationships between genes. Though it turns into a more challenging problem, we argue that partial observability would be a more natural and realistic method for handling the control of GRNs. Partial observability is a fundamental aspect of the problem / it is mostly ignored and substituted by the assumption that states of GRN are known precisely, prescribed as full observability. On the other hand, current works addressing partially observability focus on formulating algorithms for the nite horizon GRN control problem. So, in this work we explore the feasibility of realizing the problem in a partially observable setting, mainly with Partially Observable Markov Decision Processes (POMDP). We proposed a POMDP formulation for the innite horizon version of the problem. Knowing the fact that POMDP problems suer from the curse of dimensionality, we also proposed a POMDP solution method that automatically decomposes the problem by isolating dierent unrelated parts of the problem, and then solves the reduced subproblems. We also proposed a method to enrich gene expression data sets given as input to POMDP control task, because in available data sets there are thousands of genes but only tens or rarely hundreds of samples. The method is based on the idea of generating more than one model using the available data sets, and then sampling data from each of the models and nally ltering the generated samples with the help of metrics that measure compatibility, diversity and coverage of the newly generated samples.

Stochastic control problems that arise in sequential decision making applications typically assume that information used for decision-making is obtained according to a predetermined sampling schedule. In many real applications however, there is a high sampling cost associated with collecting such data. It is therefore of equal importance to determine when information should be collected as it is to decide how this information should be utilized for optimal decision-making. This type of joint optimization has been a long-standing problem in the operations research literature, and very few results regarding the structure of the optimal sampling and control policy have been published. In this thesis, the joint optimization of sampling and control is studied in the context of maintenance optimization. New theoretical results characterizing the structure of the optimal policy are established, which have practical interpretation and give new insight into the value of condition-based maintenance programs in life-cycle asset management. Applications in other areas such as healthcare decision-making and statistical process control are discussed. Statistical parameter estimation results are also developed with illustrative real-world numerical examples.

Stochastic control problems that arise in sequential decision making applications typically assume that information used for decision-making is obtained according to a predetermined sampling schedule. In many real applications however, there is a high sampling cost associated with collecting such data. It is therefore of equal importance to determine when information should be collected as it is to decide how this information should be utilized for optimal decision-making. This type of joint optimization has been a long-standing problem in the operations research literature, and very few results regarding the structure of the optimal sampling and control policy have been published. In this thesis, the joint optimization of sampling and control is studied in the context of maintenance optimization. New theoretical results characterizing the structure of the optimal policy are established, which have practical interpretation and give new insight into the value of condition-based maintenance programs in life-cycle asset management. Applications in other areas such as healthcare decision-making and statistical process control are discussed. Statistical parameter estimation results are also developed with illustrative real-world numerical examples.

Across a range of sectors, including transportation and healthcare, the use of automation to assist humans with increasingly complex tasks is also demanding that such systems are more interactive with human users. Given the role of cognitive factors in human decision-making during their interactions with automation, models enabling human cognitive state estimation and prediction could be used by autonomous systems to appropriately adapt their behavior. However, accomplishing this requires mathematical models of human cognitive state evolution that are suitable for algorithm design. In this thesis, a computational model of coupled human trust and self-confidence dynamics is proposed. The dynamics are modeled as a partially observable Markov decision process that leverages behavioral and self-report data as observations for estimation of the cognitive states. The use of an asymmetrical structure in the emission probability functions enables labeling and interpretation of the coupled cognitive states. The model is trained and validated using data collected from 340 participants. Analysis of the transition probabilities shows that the model captures nuanced effects, in terms of participants' decisions to rely on an autonomous system, that result as a function of the combination of their trust in the automation and self-confidence. Implications for the design of human-aware autonomous systems are discussed, particularly in the context of human trust and self-confidence calibration.

Unmanned aerial vehicles (UAVs) have emerged as a promising technology in search and rescue operations (SAR). UAVs have the ability to provide more timely localization, thus decreasing the crucial duration of SAR operations. Previous work have demonstrated proof-of-concept in regard to localizing missing people by utilizing received signal strength (RSS) and UAVs. The localization system is based on the assumption that the missing person wears an enabled smartphone whose Wi-Fi signal can be intercepted. This thesis proposes a two-staged path planner for UAVs, utilizing RSS-signals and an initial belief regarding the missing person's location. The objective of the first stage is to locate an RSS-signal. By dividing the search area into grids, a hierarchical solution based on several Markov decision processes (MDPs) can be formulated which takes different areas probabilities into consideration. The objective of the second stage is to isolate the RSS-signal and provide a location estimate. The environment is deemed to be partially observable, and the problem is formulated as a partially observable Markov decision process (POMDP). Two different filters, a point mass filter (PMF) and a particle filter (PF), are evaluated in regard to their ability to correctly estimate the state of the environment. The state of the environment then acts as input to a deep Q-network (DQN) which selects appropriate actions for the UAV. Thus, the DQN becomes a path planner for the UAV and the trajectory it generates is compared to trajectories generated by, among others, a greedy-policy.  Results for Stage 1 demonstrate that the path generated by the MDPs prioritizes areas with higher probability, and intuitively seems very reasonable. The results also illustrate potential drawbacks with a hierarchical solution, which potentially can be addressed by considering more factors into the problem. Simulation results for Stage 2 show that both a PMF and a PF can successfully be used to estimate the state of the environment and provide an accurate localization estimate. The PMF generated slightly more accurate estimations compared to the PF. The DQN is successful in isolating the missing person's probable location, by relatively few actions. However, it only performs marginally better than the greedy policy, indicating that it may be a complicated solution to a simpler problem.

Intelligent tutoring systems (ITSs) are computer programs that model individual learners and adapt instruction to help each learner differently. One way ITSs differ from human tutors is that few ITSs give learners a way to ask questions. When learners can ask for help, their questions have the potential to improve learning directly and also act as a new source of model data to help the ITS personalize instruction. Inquiry modeling gives ITSs the ability to answer learner questions and refine their learner models with an inexpensive new input channel. In order to support inquiry modeling, an advanced planning formalism is applied to ITS learner modeling. Partially observable Markov decision processes (POMDPs) differ from more widely used ITS architectures because they can plan complex action sequences in uncertain situations with machine learning. Tractability issues have previously precluded POMDP use in ITS models. This dissertation introduces two improvements, priority queues and observation chains, to make POMDPs scale well and encompass the large problem sizes that real-world ITSs must confront. A new ITS was created to support trainees practicing a military task in a virtual environment. The development of the Inquiry Modeling POMDP Adaptive Trainer (IMP) began with multiple formative studies on human and simulated learners that explored inquiry modeling and POMDPs in intelligent tutoring. The studies suggest the new POMDP representations will be effective in ITS domains having certain common characteristics. iv Finally, a summative study evaluated IMP’s ability to train volunteers in specific practice scenarios. IMP users achieved post-training scores averaging up to 4.5 times higher than users who practiced without support and up to twice as high as trainees who used an ablated version of IMP with no inquiry modeling. IMP’s implementation and evaluation helped explore questions about how inquiry modeling and POMDP ITSs work, while empirically demonstrating their efficacy

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