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.

Nowadays, neural network (NN) and deep learning (DL) techniques are widely adopted in many applications, including recommender systems. Given the sparse and stochastic nature of collaborative filtering (CF) data, recent works have critically analyzed the effective improvement of neural-based approaches compared to simpler and often transparent algorithms for recommendation. Previous results showed that NN and DL models can be outperformed by traditional algorithms in many tasks. Moreover, given the largely black-box nature of neural-based methods, interpretable results are not naturally obtained. Following on this debate, we first present a transparent probabilistic model that topologically organizes user and product latent classes based on the review information. In contrast to popular neural techniques for representation learning, we readily obtain a statistical, visualization-friendly tool that can be easily inspected to understand user and product characteristics from a textual-based perspective. Then, given the limitations of common embedding techniques, we investigate the possibility of using the estimated interpretable quantities as model input for a rating prediction task. To contribute to the recent debates, we evaluate our results in terms of both capacity for interpretability and predictive performances in comparison with popular text-based neural approaches. The results demonstrate that the proposed latent class representations can yield competitive predictive performances, compared to popular, but difficult-to-interpret approaches.

Visualizing data and finding patterns in data are ubiquitous problems in the sciences. Increasingly, applications seek signal and structure in a contrastive setting: a foreground dataset relative to a background dataset. For this purpose, we propose contrastive independent component analysis (cICA). This generalizes independent component analysis to independent latent variables across a foreground and background. We propose a hierarchical tensor decomposition algorithm for cICA. We study the identifiability of cICA and demonstrate its performance visualizing data and finding patterns in data, using synthetic and real-world datasets, comparing the approach to existing contrastive methods.

The Feynman-Kac Operator Expectation Estimator (FKEE) is an innovative method for estimating the target Mathematical Expectation $\mathbb{E}_{X\sim P}[f(X)]$ without relying on a large number of samples, in contrast to the commonly used Markov Chain Monte Carlo (MCMC) Expectation Estimator. FKEE comprises diffusion bridge models and approximation of the Feynman-Kac operator. The key idea is to use the solution to the Feynmann-Kac equation at the initial time $u(x_0,0)=\mathbb{E}[f(X_T)|X_0=x_0]$. We use Physically Informed Neural Networks (PINN) to approximate the Feynman-Kac operator, which enables the incorporation of diffusion bridge models into the expectation estimator and significantly improves the efficiency of using data while substantially reducing the variance. Diffusion Bridge Model is a more general MCMC method. In order to incorporate extensive MCMC algorithms, we propose a new diffusion bridge model based on the Minimum Wasserstein distance. This diffusion bridge model is universal and reduces the training time of the PINN. FKEE also reduces the adverse impact of the curse of dimensionality and weakens the assumptions on the distribution of $X$ and performance function $f$ in the general MCMC expectation estimator. The theoretical properties of this universal diffusion bridge model are also shown. Finally, we demonstrate the advantages and potential applications of this method through various concrete experiments, including the challenging task of approximating the partition function in the random graph model such as the Ising model.