Optimal experimental design (OED) provides a systematic approach to quantify and maximize the value of experimental data. Under a Bayesian approach, conventional OED maximizes the expected information gain (EIG) on model parameters. However, we are often interested in not the parameters themselves, but predictive quantities of interest (QoIs) that depend on the parameters in a nonlinear manner. We present a computational framework of predictive goal-oriented OED (GO-OED) suitable for nonlinear observation and prediction models, which seeks the experimental design providing the greatest EIG on the QoIs. In particular, we propose a nested Monte Carlo estimator for the QoI EIG, featuring Markov chain Monte Carlo for posterior sampling and kernel density estimation for evaluating the posterior-predictive density and its Kullback-Leibler divergence from the prior-predictive. The GO-OED design is then found by maximizing the EIG over the design space using Bayesian optimization. We demonstrate the effectiveness of the overall nonlinear GO-OED method, and illustrate its differences versus conventional non-GO-OED, through various test problems and an application of sensor placement for source inversion in a convection-diffusion field.

This paper studies semantic-aware communication for remote estimation of multiple Markov sources over a lossy and rate-constrained channel. Unlike most existing studies that treat all source states equally, we exploit the semantics of information and consider that the remote actuator has different tolerances for the estimation errors of different states. We aim to find an optimal scheduling policy that minimizes the long-term state-dependent costs of estimation errors under a transmission frequency constraint. We theoretically show the structure of the optimal policy by leveraging the average-cost Constrained Markov Decision Process (CMDP) theory and the Lagrangian dynamic programming. By exploiting the optimal structural results, we develop a novel policy search algorithm, termed intersection search plus relative value iteration (Insec-RVI), that can find the optimal policy using only a few iterations. To avoid the ``curse of dimensionality'' of MDPs, we propose an online low-complexity drift-plus-penalty (DPP) scheduling algorithm based on the Lyapunov optimization theorem. We also design an efficient average-cost Q-learning algorithm to estimate the optimal policy without knowing a priori the channel and source statistics. Numerical results show that continuous transmission is inefficient, and remarkably, our semantic-aware policies can attain the optimum by strategically utilizing fewer transmissions by exploiting the timing of the important information.

Lagrangian-guided Monte Carlo tree search with global dual ascent has been applied to solve large constrained partially observable Markov decision processes (CPOMDPs) online. In this work, we demonstrate that these global dual parameters can lead to myopic action selection during exploration, ultimately leading to suboptimal decision making. To address this, we introduce history-dependent dual variables that guide local action selection and are optimized with recursive dual ascent. We empirically compare the performance of our approach on a motivating toy example and two large CPOMDPs, demonstrating improved exploration, and ultimately, safer outcomes.

The current thesis aims to explore the reinforcement learning field and build on existing methods to produce improved ones to tackle the problem of learning in high-dimensional and complex environments. It addresses such goals by decomposing learning tasks in a hierarchical fashion known as Hierarchical Reinforcement Learning. We start in the first chapter by getting familiar with the Markov Decision Process framework and presenting some of its recent techniques that the following chapters use. We then proceed to build our Hierarchical Policy learning as an answer to the limitations of a single primitive policy. The hierarchy is composed of a manager agent at the top and employee agents at the lower level. In the last chapter, which is the core of this thesis, we attempt to learn lower-level elements of the hierarchy independently of the manager level in what is known as the "Eigenoption". Based on the graph structure of the environment, Eigenoptions allow us to build agents that are aware of the geometric and dynamic properties of the environment. Their decision-making has a special property: it is invariant to symmetric transformations of the environment, allowing as a consequence to greatly reduce the complexity of the learning task.

Neural network actor-critic algorithms are one of the most popular methods in deep reinforcement learning. A neural network model is trained to select the policy (the "actor") while another neural network (the "critic") is simultaneously trained to learn the value function given the actor's policy. Specifically, the actor selects an action and, given the action, a new state transition occurs according to a Markov stochastic process and a reward (a measurement of the success/failure) is observed. The critic must learn to approximate the value function - the solution to the Bellman equation - given the actor's policy. Given the critic's estimate for the value function of the current policy, the actor must be updated to improve the value function (i.e., increase the expected reward). Actor-critic algorithms are well-established methods in reinforcement learning [17, 15]; the key recent advance is using (deep) neural networks as the actor/critic and training their parameters using gradient descent methods [26, 10, 25, 2, 29]. Analysis of neural network actor-critic algorithms is challenging due to: (1) the non-convexity of the neural networks, (2) the complex feedback loop between the actor and critic (the actor determines the sequence of data samples which are used to train the critic and the critic is used to train the actor), and (3) the simultaneous online updates of both the actor and critic which lead to (3A) the distribution of the data, which depends upon the actor, constantly evolving in time and (3B) the actor being updated with a noisy, biased estimate of the value function.

The importance of considering contextual probabilities in shaping response patterns within psychological testing is underscored, despite the ubiquitous nature of order effects discussed extensively in methodological literature. Drawing from concepts such as path-dependency, first-order autocorrelation, state-dependency, and hysteresis, the present study is an attempt to address how earlier responses serve as an anchor for subsequent answers in tests, surveys, and questionnaires. Introducing the notion of non-commuting observables derived from quantum physics, I highlight their role in characterizing psychological processes and the impact of measurement instruments on participants' responses. We advocate for the utilization of first-order Markov chain modeling to capture and forecast sequential dependencies in survey and test responses. The employment of the first-order Markov chain model lies in individuals' propensity to exhibit partial focus to preceding responses, with recent items most likely exerting a substantial influence on subsequent response selection. This study contributes to advancing our understanding of the dynamics inherent in sequential data within psychological research and provides a methodological framework for conducting longitudinal analyses of response patterns of test and questionnaire.

The advent of deep reinforcement learning (DRL) has significantly advanced the field of robotics, particularly in the control and coordination of quadruped robots. However, the complexity of real-world tasks often necessitates the deployment of multi-robot systems capable of sophisticated interaction and collaboration. To address this need, we introduce the Multi-agent Quadruped Environment (MQE), a novel platform designed to facilitate the development and evaluation of multi-agent reinforcement learning (MARL) algorithms in realistic and dynamic scenarios. MQE emphasizes complex interactions between robots and objects, hierarchical policy structures, and challenging evaluation scenarios that reflect real-world applications. We present a series of collaborative and competitive tasks within MQE, ranging from simple coordination to complex adversarial interactions, and benchmark state-of-the-art MARL algorithms. Our findings indicate that hierarchical reinforcement learning can simplify task learning, but also highlight the need for advanced algorithms capable of handling the intricate dynamics of multi-agent interactions. MQE serves as a stepping stone towards bridging the gap between simulation and practical deployment, offering a rich environment for future research in multi-agent systems and robot learning. For open-sourced code and more details of MQE, please refer to https://ziyanx02.github.io/multiagent-quadruped-environment/ .

In this paper, we present an online reinforcement learning algorithm for constrained Markov decision processes with a safety constraint. Despite the necessary attention of the scientific community, considering stochastic stopping time, the problem of learning optimal policy without violating safety constraints during the learning phase is yet to be addressed. To this end, we propose an algorithm based on linear programming that does not require a process model. We show that the learned policy is safe with high confidence. We also propose a method to compute a safe baseline policy, which is central in developing algorithms that do not violate the safety constraints. Finally, we provide simulation results to show the efficacy of the proposed algorithm. Further, we demonstrate that efficient exploration can be achieved by defining a subset of the state-space called proxy set.

Target class classification is a mixed classification and transition model whose integrated goal is to assign objects to a certain, so called target or normal class. The classification process is iterative, and in each step an object in a certain class undergoes an action attached to that class, initiating the transition of the object to one of the classes. The sequence of transitions, which we call class transitions, must be designed to provide the final assignment of objects to the target class. The transition process can be described in the form of a directed graph, and the success of the final classification is mainly due to the properties of this graph. In our previous research we showed that the desirable structure of the transition graph is an oriented rooted tree with orientation towards the root vertex, which corresponds to the normal class. It is clear that the transition graph of an arbitrary algorithm (policy) may not have this property. In this paper we study the structure of realistic transition graphs, which makes it possible to find classification inconsistencies, helping to transfer it into the desired form. The medical interpretation of "dynamic treatment regime" considered in the article further clarifies the investigated framework.

With the advancements of artificial intelligence (AI), we're seeing more scenarios that require AI to work closely with other agents, whose goals and strategies might not be known beforehand. However, existing approaches for training collaborative agents often require defined and known reward signals and cannot address the problem of teaming with unknown agents that often have latent objectives/rewards. In response to this challenge, we propose teaming with unknown agents framework, which leverages kernel density Bayesian inverse learning method for active goal deduction and utilizes pre-trained, goal-conditioned policies to enable zero-shot policy adaptation. We prove that unbiased reward estimates in our framework are sufficient for optimal teaming with unknown agents. We further evaluate the framework of redesigned multi-agent particle and StarCraft II micromanagement environments with diverse unknown agents of different behaviors/rewards. Empirical results demonstrate that our framework significantly advances the teaming performance of AI and unknown agents in a wide range of collaborative scenarios.