The environments where individuals live can present diverse navigation challenges, resulting in varying navigation abilities and strategies. Inspired by differing urban layouts and the Dual Solutions Paradigm test used for human navigators, we developed a simulated navigation environment to train deep reinforcement learning agents in a shortcut usage task. We modulated the frequency of exposure to a shortcut and navigation cue, leading to the development of artificial agents with differing abilities. We examined the encoded representations in artificial neural networks driving these agents, revealing intricate dynamics in representation learning, and correlated them with shortcut use preferences. Furthermore, we demonstrated methods to analyze representations across a population of nodes, which proved effective in finding patterns in what would otherwise be noisy single-node data. These techniques may also have broader applications in studying neural activity. From our observations in representation learning dynamics, we propose insights for human navigation learning, emphasizing the importance of navigation challenges in developing strong landmark knowledge over repeated exposures to landmarks alone.

In recent times, large language models (LLMs) have made significant strides in generating computer code, blurring the lines between code created by humans and code produced by artificial intelligence (AI). As these technologies evolve rapidly, it is crucial to explore how they influence code generation, especially given the risk of misuse in areas like higher education. This paper explores this issue by using advanced classification techniques to differentiate between code written by humans and that generated by ChatGPT, a type of LLM. We employ a new approach that combines powerful embedding features (black-box) with supervised learning algorithms - including Deep Neural Networks, Random Forests, and Extreme Gradient Boosting - to achieve this differentiation with an impressive accuracy of 98%. For the successful combinations, we also examine their model calibration, showing that some of the models are extremely well calibrated. Additionally, we present white-box features and an interpretable Bayes classifier to elucidate critical differences between the code sources, enhancing the explainability and transparency of our approach. Both approaches work well but provide at most 85-88% accuracy. We also show that untrained humans solve the same task not better than random guessing. This study is crucial in understanding and mitigating the potential risks associated with using AI in code generation, particularly in the context of higher education, software development, and competitive programming.

This work starts with the intention of using mathematics to understand the intriguing vulnerability observed by ~\citet{szegedy2013} within artificial neural networks. Along the way, we will develop some novel tools with applications far outside of just the adversarial domain. We will do this while developing a rigorous mathematical framework to examine this problem. Our goal is to build out theory which can support increasingly sophisticated conjecture about adversarial attacks with a particular focus on the so called ``Dimpled Manifold Hypothesis'' by ~\citet{shamir2021dimpled}. Chapter one will cover the history and architecture of neural network architectures. Chapter two is focused on the background of adversarial vulnerability. Starting from the seminal paper by ~\citet{szegedy2013} we will develop the theory of adversarial perturbation and attack. Chapter three will build a theory of persistence that is related to Ricci Curvature, which can be used to measure properties of decision boundaries. We will use this foundation to make a conjecture relating adversarial attacks. Chapters four and five represent a sudden and wonderful digression that examines an intriguing related body of theory for spatial analysis of neural networks as approximations of kernel machines and becomes a novel theory for representing neural networks with bilinear maps. These heavily mathematical chapters will set up a framework and begin exploring applications of what may become a very important theoretical foundation for analyzing neural network learning with spatial and geometric information. We will conclude by setting up our new methods to address the conjecture from chapter 3 in continuing research.

Policy Optimization (PO) methods are among the most popular Reinforcement Learning (RL) algorithms in practice. Recently, Sherman et al. [2023a] proposed a PO-based algorithm with rate-optimal regret guarantees under the linear Markov Decision Process (MDP) model. However, their algorithm relies on a costly pure exploration warm-up phase that is hard to implement in practice. This paper eliminates this undesired warm-up phase, replacing it with a simple and efficient contraction mechanism. Our PO algorithm achieves rate-optimal regret with improved dependence on the other parameters of the problem (horizon and function approximation dimension) in two fundamental settings: adversarial losses with full-information feedback and stochastic losses with bandit feedback.

Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant to AD techniques because widely used particle filter algorithms yield an estimated likelihood function that is discontinuous as a function of the model parameters. We show how to embed two existing AD particle filter methods in a theoretical framework that provides an extension to a new class of algorithms. This new class permits a bias/variance tradeoff and hence a mean squared error substantially lower than the existing algorithms. We develop likelihood maximization algorithms suited to the Monte Carlo properties of the AD gradient estimate. Our algorithms require only a differentiable simulator for the latent dynamic system; by contrast, most previous approaches to AD likelihood maximization for particle filters require access to the system's transition probabilities. Numerical results indicate that a hybrid algorithm that uses AD to refine a coarse solution from an iterated filtering algorithm show substantial improvement on current state-of-the-art methods for a challenging scientific benchmark problem.

Central to the digital transformation of the process industry are Digital Twins (DTs), virtual replicas of physical manufacturing systems that combine sensor data with sophisticated data-based or physics-based models, or a combination thereof, to tackle a variety of industrial-relevant tasks like process monitoring, predictive control or decision support. The backbone of a DT, i.e. the concrete modelling methodologies and architectural frameworks supporting these models, are complex, diverse and evolve fast, necessitating a thorough understanding of the latest state-of-the-art methods and trends to stay on top of a highly competitive market. From a research perspective, despite the high research interest in reviewing various aspects of DTs, structured literature reports specifically focusing on unravelling the utilized learning paradigms (e.g. self-supervised learning) for DT-creation in the process industry are a novel contribution in this field. This study aims to address these gaps by (1) systematically analyzing the modelling methodologies (e.g. Convolutional Neural Network, Encoder-Decoder, Hidden Markov Model) and paradigms (e.g. data-driven, physics-based, hybrid) used for DT-creation; (2) assessing the utilized learning strategies (e.g. supervised, unsupervised, self-supervised); (3) analyzing the type of modelling task (e.g. regression, classification, clustering); and (4) identifying the challenges and research gaps, as well as, discuss potential resolutions provided.

In this dissertation I would like to guide the reader to the research on dialogue but more precisely the research I have conducted during my career since my PhD thesis. Starting from modular architectures with machine learning/deep learning and reinforcement learning to end-to-end deep neural networks. Besides my work as research associate, I also present the work I have supervised in the last years. I review briefly the state of the art and highlight the open research problems on conversational agents. Afterwards, I present my contribution to Task-Oriented Dialogues (TOD), both as research associate and as the industrial supervisor of CIFRE theses. I discuss conversational QA. Particularly, I present the work of two PhD candidates Thibault Cordier and Sebastien Montella; as well as the work of the young researcher Quentin Brabant. Finally, I present the scientific project, where I discuss about Large Language Models (LLMs) for Task-Oriented Dialogue and Multimodal Task-Oriented Dialogue.

Q-learning is a stochastic approximation version of the classic value iteration. The literature has established that Q-learning suffers from both maximization bias and slower convergence. Recently, multi-step algorithms have shown practical advantages over existing methods. This paper proposes a novel off-policy two-step Q-learning algorithms, without importance sampling. With suitable assumption it was shown that, iterates in the proposed two-step Q-learning is bounded and converges almost surely to the optimal Q-values. This study also address the convergence analysis of the smooth version of two-step Q-learning, i.e., by replacing max function with the log-sum-exp function. The proposed algorithms are robust and easy to implement. Finally, we test the proposed algorithms on benchmark problems such as the roulette problem, maximization bias problem, and randomly generated Markov decision processes and compare it with the existing methods available in literature. Numerical experiments demonstrate the superior performance of both the two-step Q-learning and its smooth variants.

The growing use of deep learning in safety-critical applications, such as medical imaging, has raised concerns about limited labeled data, where this demand is amplified as model complexity increases, posing hurdles for domain experts to annotate data. In response to this, active learning (AL) is used to efficiently train models with limited annotation costs. In the context of deep neural networks (DNNs), AL often uses confidence or probability outputs as a score for selecting the most informative samples. However, modern DNNs exhibit unreliable confidence outputs, making calibration essential. We propose an AL framework that self-calibrates the confidence used for sample selection during the training process, referred to as Confident Active Learning with Integrated CalibratiOn (CALICO). CALICO incorporates the joint training of a classifier and an energy-based model, instead of the standard softmax-based classifier. This approach allows for simultaneous estimation of the input data distribution and the class probabilities during training, improving calibration without needing an additional labeled dataset. Experimental results showcase improved classification performance compared to a softmax-based classifier with fewer labeled samples. Furthermore, the calibration stability of the model is observed to depend on the prior class distribution of the data.

The agency problem emerges in today's large scale machine learning tasks, where the learners are unable to direct content creation or enforce data collection. In this work, we propose a theoretical framework for aligning economic interests of different stakeholders in the online learning problems through contract design. The problem, termed \emph{contractual reinforcement learning}, naturally arises from the classic model of Markov decision processes, where a learning principal seeks to optimally influence the agent's action policy for their common interests through a set of payment rules contingent on the realization of next state. For the planning problem, we design an efficient dynamic programming algorithm to determine the optimal contracts against the far-sighted agent. For the learning problem, we introduce a generic design of no-regret learning algorithms to untangle the challenges from robust design of contracts to the balance of exploration and exploitation, reducing the complexity analysis to the construction of efficient search algorithms. For several natural classes of problems, we design tailored search algorithms that provably achieve $\tilde{O}(\sqrt{T})$ regret. We also present an algorithm with $\tilde{O}(T^{2/3})$ for the general problem that improves the existing analysis in online contract design with mild technical assumptions.