Related papers: Nested Optimal Transport Distances

Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…

This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…

In this paper, we present a novel approach to the generation of virtual scenarios of multivariate financial data of arbitrary length and composition of assets. With this approach, decades of realistic time-synchronized data can be simulated…

This paper systematically explores the advancements in adaptive trip route planning and travel time estimation (TTE) through Artificial Intelligence (AI). With the increasing complexity of urban transportation systems, traditional…

We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…

The rapid advancement of autonomous driving (AD) technologies has outpaced the development of robust safety evaluation methods. Conventional testing relies on exposing AD systems to vast numbers of real-world traffic scenes -- a brute-force…

Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one…

In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on $\mathbb{R}^{d}\times\mathbb{R}^{d}$ derived from suitable variational…

The primary goal of reinforcement learning is to develop decision-making policies that prioritize optimal performance without considering risk or safety. In contrast, safe reinforcement learning aims to mitigate or avoid unsafe states. This…

Urban environments pose a significant challenge for autonomous vehicles (AVs) as they must safely navigate while in close proximity to many pedestrians. It is crucial for the AV to correctly understand and predict the future trajectories of…

Capacity expansions as well as its reduction have been widely anticipated as important countermeasures for traffic congestion. Although capacity expansion had been traditionally well noticed as a congestion mitigation measure, but it was…

Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression…

We consider a setting where multiple entities inter-act with each other over time and the time-varying statuses of the entities are represented as multiple correlated time series. For example, speed sensors are deployed in different…

Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…

Optimal transport is a framework that facilitates the most efficient allocation of a limited amount of resources. However, the most efficient allocation scheme does not necessarily preserve the most fairness. In this paper, we establish a…

Diverse and realistic traffic scenarios are crucial for evaluating the AI safety of autonomous driving systems in simulation. This work introduces a data-driven method called TrafficGen for traffic scenario generation. It learns from the…

Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…

The objective of this research is how an implementation of AI algorithms in the microservices architecture enhances travel itineraries by cost, time, user preferences, and environmental sustainability. It uses machine learning models for…

This paper proposes an accelerated consensus-based distributed iterative algorithm for resource allocation and scheduling. The proposed gradient-tracking algorithm introduces an auxiliary variable to add momentum towards the optimal state.…

In this paper a novel stochastic optimization and extremum seeking algorithm is presented, one which is based on time-delayed random perturbations and step size adaptation. For the case of a one-dimensional quadratic unconstrained…