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The linear functional strategy for the regularization of inverse problems is considered. For selecting the regularization parameter therein, we propose the heuristic quasi-optimality principle and some modifications including the smoothness…
We describe a simple and systematic method for obtaining approximate sensitivity information from a chaotic dynamical system using a hierarchy of cumulant equations. The resulting forward and adjoint systems yield information about…
Stochastic optimal control (SOC) aims to direct the behavior of noisy systems and has widespread applications in science, engineering, and artificial intelligence. In particular, reward fine-tuning of diffusion and flow matching models and…
In multi-task reinforcement learning, it is possible to improve the data efficiency of training agents by transferring knowledge from other different but related tasks. Because the experiences from different tasks are usually biased toward…
Trajectory optimization of sensing robots to actively gather information of targets has received much attention in the past. It is well-known that under the assumption of linear Gaussian target dynamics and sensor models the stochastic…
The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
The increasing adoption of Reinforcement Learning in safety-critical systems domains such as autonomous vehicles, health, and aviation raises the need for ensuring their safety. Existing safety mechanisms such as adversarial training,…
End-to-end trained neural networks (NNs) are a compelling approach to autonomous vehicle control because of their ability to learn complex tasks without manual engineering of rule-based decisions. However, challenging road conditions,…
This study investigates an adaptive pricing scheme aimed at achieving an efficient state in a traffic congestion game characterized by a diverse population of road users. While the planner possesses knowledge of players' preferences, their…
Trajectory optimization using a learned model of the environment is one of the core elements of model-based reinforcement learning. This procedure often suffers from exploiting inaccuracies of the learned model. We propose to regularize…
In this work, we propose a novel end-to-end sinkhorn autoencoder with noise generator for efficient data collection simulation. Simulating processes that aim at collecting experimental data is crucial for multiple real-life applications,…
We consider the optimal control problem of steering an agent population to a desired distribution over an infinite horizon. This is an optimal transport problem over dynamical systems, which is challenging due to its high computational…
Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of…
We develop a deep learning algorithm for constructing globally accurate approximations to functional rational expectations equilibria of dynamic stochastic economies in the sequence space. We use deep neural networks to parameterize key…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
In this paper, we extend a framework that we developed earlier for coordination of connected and automated vehicles (CAVs) at a signal-free intersection to incorporate uncertainty. Using the possibly noisy observations of actual time…
Adversarial risk quantifies the performance of classifiers on adversarially perturbed data. Numerous definitions of adversarial risk -- not all mathematically rigorous and differing subtly in the details -- have appeared in the literature.…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
As the complexity of modern control systems increases, it becomes challenging to derive an accurate model of the uncertainty that affects their dynamics. Wasserstein Distributionally Robust Optimization (DRO) provides a powerful framework…