This work presents novel algorithms for learning Bayesian networks of bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in sampling k-trees (maximal graphs of treewidth k), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that k-tree. The approaches are empirically compared to each other and to state-of-the-art methods on a collection of public data sets with up to 100 variables.

This paper describes the problem of coordination of an autonomous Multi-Agent System which aims to solve the coverage planning problem in a complex environment. The considered applications are the detection and identification of objects of interest while covering an area. These tasks, which are highly relevant for space applications, are also of interest among various domains including the underwater context, which is the focus of this study. In this context, coverage planning is traditionally modelled as a Markov Decision Process where a coordinated MAS, a swarm of heterogeneous autonomous underwater vehicles, is required to survey an area and search for objects. This MDP is associated with several challenges: environment uncertainties, communication constraints, and an ensemble of hazards, including time-varying and unpredictable changes in the underwater environment. MARL algorithms can solve highly non-linear problems using deep neural networks and display great scalability against an increased number of agents. Nevertheless, most of the current results in the underwater domain are limited to simulation due to the high learning time of MARL algorithms. For this reason, a novel strategy is introduced to accelerate this convergence rate by incorporating biologically inspired heuristics to guide the policy during training. The PSO method, which is inspired by the behaviour of a group of animals, is selected as a heuristic. It allows the policy to explore the highest quality regions of the action and state spaces, from the beginning of the training, optimizing the exploration/exploitation trade-off. The resulting agent requires fewer interactions to reach optimal performance. The method is applied to the MSAC algorithm and evaluated for a 2D covering area mission in a continuous control environment.

This paper introduces a unified theoretical framework for modeling temporal memory dynamics, combining concepts from temporal logic, memory decay models, and hierarchical contexts. The framework formalizes the evolution of propositions over time using linear and branching temporal models, incorporating exponential decay (Ebbinghaus forgetting curve) and reactivation mechanisms via Bayesian updating. The hierarchical organization of memory is represented using directed acyclic graphs to model recall dependencies and interference. Novel insights include feedback dynamics, recursive influences in memory chains, and the integration of entropy-based recall efficiency. This approach provides a foundation for understanding memory processes across cognitive and computational domains. Let t R represent a temporal parameter.

The Bayesian Cram\'er-Rao bound (BCRB) is a crucial tool in signal processing for assessing the fundamental limitations of any estimation problem as well as benchmarking within a Bayesian frameworks. However, the BCRB cannot be computed without full knowledge of the prior and the measurement distributions. In this work, we propose a fully learned Bayesian Cram\'er-Rao bound (LBCRB) that learns both the prior and the measurement distributions. Specifically, we suggest two approaches to obtain the LBCRB: the Posterior Approach and the Measurement-Prior Approach. The Posterior Approach provides a simple method to obtain the LBCRB, whereas the Measurement-Prior Approach enables us to incorporate domain knowledge to improve the sample complexity and {interpretability}. To achieve this, we introduce a Physics-encoded score neural network which enables us to easily incorporate such domain knowledge into a neural network. We {study the learning} errors of the two suggested approaches theoretically, and validate them numerically. We demonstrate the two approaches on several signal processing examples, including a linear measurement problem with unknown mixing and Gaussian noise covariance matrices, frequency estimation, and quantized measurement. In addition, we test our approach on a nonlinear signal processing problem of frequency estimation with real-world underwater ambient noise.

Ground truth labels/outcomes are critical for advancing scientific and engineering applications, e.g., evaluating the treatment effect of an intervention or performance of a predictive model. Since randomly sampling inputs for labeling can be prohibitively expensive, we introduce an adaptive labeling framework where measurement effort can be reallocated in batches. We formulate this problem as a Markov decision process where posterior beliefs evolve over time as batches of labels are collected (state transition), and batches (actions) are chosen to minimize uncertainty at the end of data collection. We design a computational framework that is agnostic to different uncertainty quantification approaches including those based on deep learning, and allows a diverse array of policy gradient approaches by relying on continuous policy parameterizations. On real and synthetic datasets, we demonstrate even a one-step lookahead policy can substantially outperform common adaptive labeling heuristics, highlighting the virtue of planning. On the methodological side, we note that standard REINFORCE-style policy gradient estimators can suffer high variance since they rely only on zeroth order information. We propose a direct backpropagation-based approach, Smoothed-Autodiff, based on a carefully smoothed version of the original non-differentiable MDP. Our method enjoys low variance at the price of introducing bias, and we theoretically and empirically show that this trade-off can be favorable.

In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation model. Commonly, this process is done using a generative image model that can guide the reconstruction towards solutions that appear natural. The success of diffusion models over the last few years has made them a leading candidate for this task. However, the sequential nature of diffusion models makes this conditional sampling process challenging. Furthermore, since diffusion models are often defined in the latent space of an autoencoder, the encoder-decoder transformations introduce additional difficulties. Here, we suggest a novel sampling method based on sequential Monte Carlo (SMC) in the latent space of diffusion models. We use the forward process of the diffusion model to add additional auxiliary observations and then perform an SMC sampling as part of the backward process. Empirical evaluations on ImageNet and FFHQ show the benefits of our approach over competing methods on various inverse problem tasks.

Off-policy evaluation (OPE) is a critical challenge in robust decision-making that seeks to assess the performance of a new policy using data collected under a different policy. However, the existing OPE methodologies suffer from several limitations arising from statistical uncertainty as well as causal considerations. In this thesis, we address these limitations by presenting three different works. Firstly, we consider the problem of high variance in the importance-sampling-based OPE estimators. We introduce the Marginal Ratio (MR) estimator, a novel OPE method that reduces variance by focusing on the marginal distribution of outcomes rather than direct policy shifts, improving robustness in contextual bandits. Next, we propose Conformal Off-Policy Prediction (COPP), a principled approach for uncertainty quantification in OPE that provides finite-sample predictive intervals, ensuring robust decision-making in risk-sensitive applications. Finally, we address causal unidentifiability in off-policy decision-making by developing novel bounds for sequential decision settings, which remain valid under arbitrary unmeasured confounding. We apply these bounds to assess the reliability of digital twin models, introducing a falsification framework to identify scenarios where model predictions diverge from real-world behaviour. Our contributions provide new insights into robust decision-making under uncertainty and establish principled methods for evaluating policies in both static and dynamic settings.

Heterogeneity poses a fundamental challenge for many real-world large-scale decision-making problems but remains largely understudied. In this paper, we study the fully heterogeneous setting of a prominent class of such problems, known as weakly-coupled Markov decision processes (WCMDPs). Each WCMDP consists of $N$ arms (or subproblems), which have distinct model parameters in the fully heterogeneous setting, leading to the curse of dimensionality when $N$ is large. We show that, under mild assumptions, a natural adaptation of the ID policy, although originally proposed for a homogeneous special case of WCMDPs, in fact achieves an $O(1/\sqrt{N})$ optimality gap in long-run average reward per arm for fully heterogeneous WCMDPs as $N$ becomes large. This is the first asymptotic optimality result for fully heterogeneous average-reward WCMDPs. Our techniques highlight the construction of a novel projection-based Lyapunov function, which witnesses the convergence of rewards and costs to an optimal region in the presence of heterogeneity.

Under what conditions can capable AI agents efficiently align their actions with human preferences? More specifically, when they are proficient enough to collaborate with us, how long does coordination take, and when is it computationally feasible? These foundational questions of AI alignment help define what makes an AI agent ``sufficiently safe'' and valuable to humans. Since such generally capable systems do not yet exist, a theoretical analysis is needed to establish when guarantees hold -- and what they even are. We introduce a game-theoretic framework that generalizes prior alignment approaches with fewer assumptions, allowing us to analyze the computational complexity of alignment across $M$ objectives and $N$ agents, providing both upper and lower bounds. Unlike previous work, which often assumes common priors, idealized communication, or implicit tractability, our framework formally characterizes the difficulty of alignment under minimal assumptions. Our main result shows that even when agents are fully rational and computationally \emph{unbounded}, alignment can be achieved with high probability in time \emph{linear} in the task space size. Therefore, in real-world settings, where task spaces are often \emph{exponential} in input length, this remains impractical. More strikingly, our lower bound demonstrates that alignment is \emph{impossible} to speed up when scaling to exponentially many tasks or agents, highlighting a fundamental computational barrier to scalable alignment. Relaxing these idealized assumptions, we study \emph{computationally bounded} agents with noisy messages (representing obfuscated intent), showing that while alignment can still succeed with high probability, it incurs additional \emph{exponential} slowdowns in the task space size, number of agents, and number of tasks. We conclude by identifying conditions that make alignment more feasible.

While recommender systems (RSs) traditionally rely on extensive individual user data, regulatory and technological shifts necessitate reliance on aggregated user information. This shift significantly impacts the recommendation process, requiring RSs to engage in intensive exploration to identify user preferences. However, this approach risks user churn due to potentially unsatisfactory recommendations. In this paper, we propose a model that addresses the dual challenges of leveraging aggregated user information and mitigating churn risk. Our model assumes that the RS operates with a probabilistic prior over user types and aggregated satisfaction levels for various content types. We demonstrate that optimal policies naturally transition from exploration to exploitation in finite time, develop a branch-and-bound algorithm for computing these policies, and empirically validate its effectiveness.