Related papers: On Optimal Stochastic Ballistic Transports
This article reviews the use of first order convex optimization schemes to solve the discretized dynamic optimal transport problem, initially proposed by Benamou and Brenier. We develop a staggered grid discretization that is well adapted…
Recent studies have extended the use of the stochastic Hamilton-Jacobi-Bellman (HJB) equation to include complex variables for deriving quantum mechanical equations. However, these studies often assume that it is valid to apply the HJB…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
We consider a class of stochastic optimal control problems for discrete-time stochastic linear systems which seek for control policies that will steer the probability distribution of the terminal state of the system close to a desired…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
Inspired by the Boltzmann kinetics, we propose a collision-based dynamics with a Monte Carlo solution algorithm that approximates the solution of the multi-marginal optimal transport problem via randomized pairwise swapping of sample…
We discuss stochastic representations of advection diffusion equations with variable diffusivity, stochastic integrals of motion and generalized relative entropies.
We introduce and investigate properties of a variant of the semi-discrete optimal transport problem. In this problem, one is given an absolutely continuous source measure and cost function, along with a finite set which will be the support…
We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this…
This paper proposes a data-driven distributionally robust shortest path (DRSP) model where the distribution of the travel time in the transportation network can only be partially observed through a finite number of samples. Specifically, we…
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence…
Controlling the evolution of a many-body stochastic system from a disordered reference state to a structured target ensemble, characterized empirically through samples, arises naturally in non-equilibrium statistical mechanics and…
We consider the optimal transportation problem on a globally hyperbolic spacetime for some cost function $c_2$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is the…
The multi-path Traveling Salesman Problem with stochastic travel costs arises in hybrid vehicle routing applications designed for Smart City and City Logistics, where multiple paths exist between each pair of locations. Travel times along…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
We study the connections between Physarum Dynamics and Dynamic Monge Kantorovich (DMK) Optimal Transport algorithms for the solution of Basis Pursuit problems. We show the equivalence between these two models and unveil their dynamic…
We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential…
In this paper we study a representation problem first considered in a simpler version by Bank and El Karoui [2004]. A key ingredient to this problem is a random measure $\mu$ on the time axis which in the present paper is allowed to have…