Related papers: Approximating optimal transport with linear progra…
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…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
Given facilities with capacities and clients with penalties and demands, the transportation problem with market choice consists in finding the minimum-cost way to partition the clients into unserved clients, paying the penalties, and into…
In this work, we provide faster algorithms for approximating the optimal transport distance, e.g. earth mover's distance, between two discrete probability distributions $\mu, \nu \in \Delta^n$. Given a cost function $C : [n] \times [n] \to…
Optimal mass transport is described by an approximation of transport cost via semi-discrete costs. The notions of optimal partition and optimal strong partition are given as well. We also suggest an algorithm for computation of Optimal…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…
In this paper, we consider a dynamic equilibrium transportation problem. There is a fixed number of cars moving from origin to destination areas. Preferences for arrival times are expressed as a cost of arriving before or after the…
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has…
We consider approximations formed by the sum of a linear combination of given functions enhanced by ridge functions -- a Linear/Ridge expansion. For an explicitly or implicitly given function, we reformulate finding a best Linear/Ridge…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
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…
This paper studies line planning for urban bus networks that face multiple resource limits such as budget, labor, and emission caps while using heterogeneous fleets. The objective is to maximize total reward from serving passengers by…
We propose an entropic approximation approach for optimal transportation problems with a supremal cost. We establish $\Gamma$-convergence for suitably chosen parameters for the entropic penalization and that this procedure selects…
We study the consequences of the equivalence between the least gradient problem and a boundary-to-boundary optimal transport problem in two dimensions. We extend the relationship between the two problems to their respective dual problems,…
We study real-time routing policies in smart transit systems, where the platform has a combination of cars and high-capacity vehicles (e.g., buses or shuttles) and seeks to serve a set of incoming trip requests. The platform can use its…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…