Related papers: Algorithms for constrained optimal transport
Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…
Motion planning is still an open problem for many disciplines, e.g., robotics, autonomous driving, due to their need for high computational resources that hinder real-time, efficient decision-making. A class of methods striving to provide…
Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…
We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most $n$ components. We show…
Transportation cost is an attractive similarity measure between probability distributions due to its many useful theoretical properties. However, solving optimal transport exactly can be prohibitively expensive. Therefore, there has been…
We study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem…
We propose a new regularized optimal transport (OT) formulation, termed sliced-regularized optimal transport (SROT). Unlike entropic OT (EOT), which regularizes the transport plan toward an independent coupling, SROT regularizes it toward a…
Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…
We introduce fast algorithms for generalized unnormalized optimal transport. To handle densities with different total mass, we consider a dynamic model, which mixes the $L^p$ optimal transport with $L^p$ distance. For $p=1$, we derive the…
Sampling-based model predictive control methods like MPPI and CEM are essential for real-time control of nonlinear robotic systems, particularly where discontinuous dynamics preclude gradient-based optimization. However, these methods…
We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…
We consider the one-to-one Pickup and Delivery Problem (PDP) in Euclidean Space with arbitrary dimension $d$ where $n$ transportation requests are picked i.i.d. with a separate origin-destination pair for each object to be moved. First, we…
Recently, Sinkhorn's algorithm was applied for approximately solving linear programs emerging from optimal transport very efficiently. This was accomplished by formulating a regularized version of the linear program as Bregman projection…
An optimal transport (OT) problem seeks to find the cheapest mapping between two distributions with equal total density, given the cost of transporting density from one place to another. Unbalanced OT allows for different total density in…
With rapid population growth and urban development, traffic congestion has become an inescapable issue, especially in large cities. Many congestion reduction strategies have been proposed in the past, ranging from roadway extension to…
Although electric vehicles are considered a viable solution to reduce greenhouse gas emissions, their uncoordinated charging could have adverse effects on power system operation. Nevertheless, the task of optimal electric vehicle charging…
We present a method based on optimal transport to remove arbitrage opportunities within a finite set of option prices. The method is notably intended for regulatory stress-tests, which require applying significant local distortions to…
Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…
We study the problem of optimally routing plug-in electric and conventional fuel vehicles on a city level. In our model, commuters selfishly aim to minimize a local cost that combines travel time, from a fixed origin to a desired…
Consider the Monge-Kantorovich problem of transporting densities $\rho_0$ to $\rho_1$ on $\mathbb{R}^d$ with a strictly convex cost function. A popular relaxation of the problem is the one-parameter family called the entropic cost problem.…