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To overcome the sim-to-real gap in reinforcement learning (RL), learned policies must maintain robustness against environmental uncertainties. While robust RL has been widely studied in single-agent regimes, in multi-agent environments, the…

Various applications involve assigning discrete label values to a collection of objects based on some pairwise noisy data. Due to the discrete---and hence nonconvex---structure of the problem, computing the optimal assignment (e.g.~maximum…

A common method for deriving non-parametric tests is to reformulate a parametric test in terms of sample ranks. Despite being distribution free (even in finite samples), the resulting tests often display remarkable asymptotic power…

We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…

We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant…

The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…

Recent advancements have shown that reinforcement learning (RL) can substantially improve the reasoning abilities of large language models (LLMs). The effectiveness of such RL training, however, depends critically on the exploration space…

This paper investigates the location-based relay selection problem, where the source node chooses its relay from a set of spatially deployed decode-and-forward relays. The advantages of location-based relay selection are the elimination of…

Robust reinforcement learning (Robust RL) seeks to handle epistemic uncertainty in environment dynamics, but existing approaches often rely on nested min--max optimization, which is computationally expensive and yields overly conservative…

The practicality of reinforcement learning algorithms has been limited due to poor scaling with respect to the problem size, as the sample complexity of learning an $\epsilon$-optimal policy is $\tilde{\Omega}\left(|S||A|H^3 /…

We consider data-based predictive control based on behavioral systems theory. In the linear setting this means that a system is described as a subspace of trajectories, and predictive control can be formulated using a projection onto the…

In this paper we study the problem of measuring and testing joint independence for a collection of multivariate random variables. Using the emerging theory of optimal transport (OT) based multivariate ranks, we propose a distribution-free…

We propose a class of rank-based procedures for testing that the shape matrix $\mathbf{V}$ of an elliptical distribution (with unspecified center of symmetry, scale and radial density) has some fixed value ${\mathbf{V}}_0$; this includes,…

Diversity schemes play a vital role in improving the performance of ultra-reliable communication systems by transmitting over two or more communication channels to combat fading and co-channel interference. Determining an appropriate…

Under Water Sensor Networks (UWSN) have different characteristics than terrestrial sensor networks, so routing protocols developed for terrestrial networks are not suitable for UWSN. Underwater routing is comprehended by the underlying…

Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…

The present work extends the randomized shortest-paths framework (RSP), interpolating between shortest-path and random-walk routing in a network, in three directions. First, it shows how to deal with equality constraints on a subset of…

Equivariant neural networks have shown great success in reinforcement learning, improving sample efficiency and generalization when there is symmetry in the task. However, in many problems, only approximate symmetry is present, which makes…

We describe the use of an unsupervised Random Forest for similarity learning and improved unsupervised anomaly detection. By training a Random Forest to discriminate between real data and synthetic data sampled from a uniform distribution…

Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…