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We introduce Markov Random Geometric Graphs (MRGGs), a growth model for temporal dynamic networks. It is based on a Markovian latent space dynamic: consecutive latent points are sampled on the Euclidean Sphere using an unknown Markov…

This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…

We (claim to) prove the extremely surprising fact that NP=RP. It is achieved by creating a Fully Polynomial-Time Randomized Approximation Scheme (FPRAS) for approximately counting the number of independent sets in bounded degree graphs,…

Imitation learning is a powerful machine learning algorithm for a robot to acquire manipulation skills. Nevertheless, many real-world manipulation tasks involve precise and dexterous robot-object interactions, which make it difficult for…

Reinforcement learning algorithms assume that observations satisfy the Markov property, yet real-world sensors frequently violate this assumption through correlated noise, latency, or partial observability. Standard performance metrics…

Reinforcement learning (RL) problems are often phrased in terms of Markov decision processes (MDPs). In this thesis we go beyond MDPs and consider RL in environments that are non-Markovian, non-ergodic and only partially observable. Our…

Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…

Reinforcement Learning (RL) algorithms are known to suffer from the curse of dimensionality, which refers to the fact that large-scale problems often lead to exponentially high sample complexity. A common solution is to use deep neural…

We numerically investigate a mean-field Bayesian approach with the assistance of the Markov chain Monte Carlo method to estimate motion velocity fields and probabilistic models simultaneously in consecutive digital images described by…

Discrete-time Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there…

Metric graphs are structures obtained by associating edges in a standard graph with segments of the real line and gluing these segments at the vertices of the graph. The resulting structure has a natural metric that allows for the study of…

In deep learning, it is common to use more network parameters than training points. In such scenarioof over-parameterization, there are usually multiple networks that achieve zero training error so that thetraining algorithm induces an…

Non-stationary environments are challenging for reinforcement learning algorithms. If the state transition and/or reward functions change based on latent factors, the agent is effectively tasked with optimizing a behavior that maximizes…

Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems,…

The advent of deep learning and recurrent neural networks revolutionized the field of time-series processing. Therefore, recent research on spectrum prediction has focused on the use of these tools. However, spectrum prediction, which…

This paper addresses the problem of optimal control of robotic sensing systems aimed at autonomous information gathering in scenarios such as environmental monitoring, search and rescue, and surveillance and reconnaissance. The information…

The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…

We provide an efficient algorithm to generate random samples from the bounded kth order statistic in a sample of independent, but not necessarily identically distributed, random variables. The bounds can be upper or lower bounds and need…

Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…

Providing generalization guarantees for stochastic optimization algorithms remains a key challenge in learning theory. Recently, numerous works demonstrated the impact of the geometric properties of optimization trajectories on…