Related papers: Nested Optimal Transport Distances
We study optimal transport for stationary stochastic processes taking values in finite spaces. In order to reflect the stationarity of the underlying processes, we restrict attention to stationary couplings, also known as joinings. The…
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…
The geometric transportation problem takes as input a set of points $P$ in $d$-dimensional Euclidean space and a supply function $\mu : P \to \mathbb{R}$. The goal is to find a transportation map, a non-negative assignment $\tau : P \times…
Motion behaviour is driven by several factors -- goals, presence and actions of neighbouring agents, social relations, physical and social norms, the environment with its variable characteristics, and further. Most factors are not directly…
For highly automated driving above SAE level~3, behavior generation algorithms must reliably consider the inherent uncertainties of the traffic environment, e.g. arising from the variety of human driving styles. Such uncertainties can…
Distributed optimization finds applications in large-scale machine learning, data processing and classification over multi-agent networks. In real-world scenarios, the communication network of agents may encounter latency that may affect…
Generating synthetic financial time series data that accurately reflects real-world market dynamics holds tremendous potential for various applications, including portfolio optimization, risk management, and large scale machine learning. We…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
Generative adversarial networks (GANs) have achieved significant success in generating real-valued data. However, the discrete nature of text hinders the application of GAN to text-generation tasks. Instead of using the standard GAN…
This paper presents a Newton-based stochastic extremum-seeking control method for real-time optimization in multi-input systems with distinct input delays. It combines predictor-based feedback and Hessian inverse estimation via stochastic…
This work discusses the benefits of having multiple simulated environments with different degrees of realism for the development of algorithms in scenarios populated by autonomous nodes capable of communication and mobility. This approach…
A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary…
The design of multitarget rendezvous missions requires a method to quickly and accurately approximate the optimal transfer between any two rendezvous targets. In this paper, a deep neural network (DNN)-based method is proposed for quickly…
In the vehicular mixed reality (MR) Metaverse, the distance between physical and virtual entities can be overcome by fusing the physical and virtual environments with multi-dimensional communications in autonomous driving systems. Assisted…
Training robots in simulation requires diverse 3D scenes that reflect the specific challenges of downstream tasks. However, scenes that satisfy strict task requirements, such as high-clutter environments with plausible spatial arrangement,…
The nested distance builds on the Wasserstein distance to quantify the difference of stochastic processes, including also the information modelled by filtrations. The Sinkhorn divergence is a relaxation of the Wasserstein distance, which…
Distributed optimization and learning algorithms are designed to operate over large scale networks enabling processing of vast amounts of data effectively and efficiently. One of the main challenges for ensuring a smooth learning process in…
Accurate trajectory prediction is essential for the safety and efficiency of autonomous driving. Traditional models often struggle with real-time processing, capturing non-linearity and uncertainty in traffic environments, efficiency in…
In this paper we present an algorithm for optimal processing of time-dependent sequenced route queries in road networks, i.e., given a road network where the travel time over an edge is time-dependent and a given ordered list of categories…
Best-of-$N$ reasoning improves the accuracy of language models in solving complex tasks by sampling multiple candidate solutions and then selecting the best one based on some criteria. A critical bottleneck for this strategy is the output…