Critical infrastructures face demanding challenges due to natural and human-generated threats, such as pandemics, workforce shortages or cyber-attacks, which might severely compromise service quality. To improve system resilience, decision-makers would need intelligent tools for quick and efficient resource allocation. This article explores an agent-based simulation model that intends to capture a part of the complexity of critical infrastructure systems, particularly considering the interdependencies of healthcare systems with information and telecommunication systems. Such a model enables to implement a simulation-based optimization approach in which the exposure of critical systems to risks is evaluated, while comparing the mitigation effects of multiple tactical and strategical decision alternatives to enhance their resilience. The proposed model is designed to be parameterizable, to enable adapting it to risk scenarios with different severity, and it facilitates the compilation of relevant performance indicators enabling monitoring at both agent level and system level. To validate the agent-based model, a literature-supported methodology has been used to perform cross-validation, sensitivity analysis and test the usefulness of the proposed model through a use case. The use case analyzes the impact of a concurrent pandemic and a cyber-attack on a hospital and compares different resiliency-enhancing countermeasures using contingency tables. Overall, the use case illustrates the feasibility and versatility of the proposed approach to enhance resiliency.

Consider a $k$-SAT formula $\Phi$ where every variable appears at most $d$ times, and let $\sigma$ be a satisfying assignment of $\Phi$ sampled proportionally to $e^{\beta m(\sigma)}$ where $m(\sigma)$ is the number of variables set to true and $\beta$ is a real parameter. Given $\Phi$ and $\sigma$, can we learn the value of $\beta$ efficiently? This problem falls into a recent line of works about single-sample ("one-shot") learning of Markov random fields. The $k$-SAT setting we consider here was recently studied by Galanis, Kandiros, and Kalavasis (SODA'24) where they showed that single-sample learning is possible when roughly $d\leq 2^{k/6.45}$ and impossible when $d\geq (k+1) 2^{k-1}$. Crucially, for their impossibility results they used the existence of unsatisfiable instances which, aside from the gap in $d$, left open the question of whether the feasibility threshold for one-shot learning is dictated by the satisfiability threshold of $k$-SAT formulas of bounded degree. Our main contribution is to answer this question negatively. We show that one-shot learning for $k$-SAT is infeasible well below the satisfiability threshold; in fact, we obtain impossibility results for degrees $d$ as low as $k^2$ when $\beta$ is sufficiently large, and bootstrap this to small values of $\beta$ when $d$ scales exponentially with $k$, via a probabilistic construction. On the positive side, we simplify the analysis of the learning algorithm and obtain significantly stronger bounds on $d$ in terms of $\beta$. In particular, for the uniform case $\beta\rightarrow 0$ that has been studied extensively in the sampling literature, our analysis shows that learning is possible under the condition $d\lesssim 2^{k/2}$. This is nearly optimal (up to constant factors) in the sense that it is known that sampling a uniformly-distributed satisfying assignment is NP-hard for $d\gtrsim 2^{k/2}$.

We introduce Social Bayesian Optimization (SBO), a vote-efficient algorithm for consensus-building in collective decision-making. In contrast to single-agent scenarios, collective decision-making encompasses group dynamics that may distort agents' preference feedback, thereby impeding their capacity to achieve a social-influence-free consensus -- the most preferable decision based on the aggregated agent utilities. We demonstrate that under mild rationality axioms, reaching social-influence-free consensus using noisy feedback alone is impossible. To address this, SBO employs a dual voting system: cheap but noisy public votes (e.g., show of hands in a meeting), and more accurate, though expensive, private votes (e.g., one-to-one interview). We model social influence using an unknown social graph and leverage the dual voting system to efficiently learn this graph. Our theoretical findigns show that social graph estimation converges faster than the black-box estimation of agents' utilities, allowing us to reduce reliance on costly private votes early in the process. This enables efficient consensus-building primarily through noisy public votes, which are debiased based on the estimated social graph to infer social-influence-free feedback. We validate the efficacy of SBO across multiple real-world applications, including thermal comfort, team building, travel negotiation, and energy trading collaboration.

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Current solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and Variational Inference (VI), which need to be re-run whenever new observations are available. Amortization, through conditional estimation, is a viable strategy to alleviate such difficulties and has been the guiding principle behind simulation-based inference, neural processes and in-context methods using pre-trained models. In this work, we conduct a thorough comparative analysis of amortized in-context Bayesian posterior estimation methods from the lens of different optimization objectives and architectural choices. Such methods train an amortized estimator to perform posterior parameter inference by conditioning on a set of data examples passed as context to a sequence model such as a transformer. In contrast to language models, we leverage permutation invariant architectures as the true posterior is invariant to the ordering of context examples. Our empirical study includes generalization to out-of-distribution tasks, cases where the assumed underlying model is misspecified, and transfer from simulated to real problems. Subsequently, it highlights the superiority of the reverse KL estimator for predictive problems, especially when combined with the transformer architecture and normalizing flows.

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption, current state-of-the-art samplers still struggle to navigate the complex and highly multimodal posteriors of BNNs. As a consequence, sampling still requires considerably longer inference times than non-Bayesian methods even for small neural networks, despite recent advances in making software implementations more efficient. Besides the difficulty of finding high-probability regions, the time until samplers provide sufficient exploration of these areas remains unpredictable. To tackle these challenges, we introduce an ensembling approach that leverages strategies from optimization and a recently proposed sampler called Microcanonical Langevin Monte Carlo (MCLMC) for efficient, robust and predictable sampling performance. Compared to approaches based on the state-of-the-art No-U-Turn Sampler, our approach delivers substantial speedups up to an order of magnitude, while maintaining or improving predictive performance and uncertainty quantification across diverse tasks and data modalities. The suggested Microcanonical Langevin Ensembles and modifications to MCLMC additionally enhance the method's predictability in resource requirements, facilitating easier parallelization. All in all, the proposed method offers a promising direction for practical, scalable inference for BNNs.

Identification of protein-protein interactions (PPIs) helps derive cellular mechanistic understanding, particularly in the context of complex conditions such as neurodegenerative disorders, metabolic syndromes, and cancer. Large Language Models (LLMs) have demonstrated remarkable potential in predicting protein structures and interactions via automated mining of vast biomedical literature; yet their inherent uncertainty remains a key challenge for deriving reproducible findings, critical for biomedical applications. In this study, we present an uncertainty-aware adaptation of LLMs for PPI analysis, leveraging fine-tuned LLaMA-3 and BioMedGPT models. To enhance prediction reliability, we integrate LoRA ensembles and Bayesian LoRA models for uncertainty quantification (UQ), ensuring confidence-calibrated insights into protein behavior. Our approach achieves competitive performance in PPI identification across diverse disease contexts while addressing model uncertainty, thereby enhancing trustworthiness and reproducibility in computational biology. These findings underscore the potential of uncertainty-aware LLM adaptation for advancing precision medicine and biomedical research.

Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear time-invariant responses, which are nonlinear only in initial conditions. This linearity allows us to tractably quantify forecasting and representational uncertainty, simultaneously alleviating the challenge of computing the distribution of trajectories from a GP-based dynamical system and enabling a new probabilistic treatment of learning Koopman operator representations. Using a trajectory-based equivariance -- which we refer to as \textit{Koopman equivariance} -- we obtain a GP model with enhanced generalization capabilities. To allow for large-scale regression, we equip our framework with variational inference based on suitable inducing points. Experiments demonstrate on-par and often better forecasting performance compared to kernel-based methods for learning dynamical systems.

Conformal prediction methods create prediction bands with distribution-free guarantees but do not explicitly capture epistemic uncertainty, which can lead to overconfident predictions in data-sparse regions. Although recent conformal scores have been developed to address this limitation, they are typically designed for specific tasks, such as regression or quantile regression. Moreover, they rely on particular modeling choices for epistemic uncertainty, restricting their applicability. We introduce $\texttt{EPICSCORE}$, a model-agnostic approach that enhances any conformal score by explicitly integrating epistemic uncertainty. Leveraging Bayesian techniques such as Gaussian Processes, Monte Carlo Dropout, or Bayesian Additive Regression Trees, $\texttt{EPICSCORE}$ adaptively expands predictive intervals in regions with limited data while maintaining compact intervals where data is abundant. As with any conformal method, it preserves finite-sample marginal coverage. Additionally, it also achieves asymptotic conditional coverage. Experiments demonstrate its good performance compared to existing methods. Designed for compatibility with any Bayesian model, but equipped with distribution-free guarantees, $\texttt{EPICSCORE}$ provides a general-purpose framework for uncertainty quantification in prediction problems.

In decentralized multi-agent deep reinforcement learning (MADRL), communication can help agents to gain a better understanding of the environment to better coordinate their behaviors. Nevertheless, communication may involve uncertainty, which potentially introduces variance to the learning of decentralized agents. In this paper, we focus on a specific decentralized MADRL setting with communication and conduct a theoretical analysis to study the variance that is caused by communication in policy gradients. We propose modular techniques to reduce the variance in policy gradients during training. We adopt our modular techniques into two existing algorithms for decentralized MADRL with communication and evaluate them on multiple tasks in the StarCraft Multi-Agent Challenge and Traffic Junction domains. The results show that decentralized MADRL communication methods extended with our proposed techniques not only achieve high-performing agents but also reduce variance in policy gradients during training.

In average reward Markov decision processes, state-of-the-art algorithms for regret minimization follow a well-established framework: They are model-based, optimistic and episodic. First, they maintain a confidence region from which optimistic policies are computed using a well-known subroutine called Extended Value Iteration (EVI). Second, these policies are used over time windows called episodes, each ended by the Doubling Trick (DT) rule or a variant thereof. In this work, without modifying EVI, we show that there is a significant advantage in replacing (DT) by another simple rule, that we call the Vanishing Multiplicative (VM) rule. When managing episodes with (VM), the algorithm's regret is, both in theory and in practice, as good if not better than with (DT), while the one-shot behavior is greatly improved. More specifically, the management of bad episodes (when sub-optimal policies are being used) is much better under (VM) than (DT) by making the regret of exploration logarithmic rather than linear. These results are made possible by a new in-depth understanding of the contrasting behaviors of confidence regions during good and bad episodes.