Related papers: Control-affine Schr\"odinger Bridge and Generalize…
We study a martingale Schr\"odinger bridge problem: given two probability distributions, find their martingale coupling with minimal relative entropy. Our main result provides Schr\"odinger potentials for this coupling. Namely, under…
Quantum counterparts of Schrodinger's classical bridge problem have been around for the better part of half a century. During that time, several quantum approaches to this multifaceted classical problem have been introduced. In the present…
We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics. Since the direct Schr\"odinger bridge between Gaussian mixtures is generally not available in closed form, we introduce a…
We study a semimartingale optimal transport problem interpolating between the Schr\"odinger bridge and the stretched Brownian motion associated with the Bass solution of the Skorokhod embedding problem. The cost combines an entropy term on…
We propose formulating the finite-horizon stochastic optimal control problem for colloidal self-assembly in the space of probability density functions (PDFs) of the underlying state variables (namely, order parameters). The control…
Schr\"{o}dinger bridge is a diffusion process that steers a given distribution to another in a prescribed time while minimizing the effort to do so. It can be seen as the stochastic dynamical version of the optimal mass transport, and has…
We address the problem of reshaping light in the Schr\"odinger optics regime from the perspective of optimal control theory. In technological applications, Schr\"odinger optics is often used to model a slowly-varying amplitude of a…
We propose a procedure for estimating the Schr\"odinger bridge between two probability distributions. Unlike existing approaches, our method does not require iteratively simulating forward and backward diffusions or training neural networks…
This paper is addressed to studying the exact controllability for stochastic Schr\"{o}dinger equations by two controls. One is a boundary control in the drift term and the other is an internal control in the diffusion term. By means of the…
We propose a variational formulation of an inverse problem in continuous-time stochastic control, aimed at identifying control costs consistent with a given distribution over trajectories. The formulation is based on minimizing the…
Large-size populations consisting of a continuum of identical and non-cooperative agents with stochastic dynamics are useful in modeling various biological and engineered systems. This paper addresses the stochastic control problem of…
The \emph{Schr\"odinger problem} is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schr\"odinger as the problem of describing the most likely evolution of…
In this work, we study the mean field Schr\"odinger problem from a purely probabilistic point of view by exploiting its connection to stochastic control theory for McKean-Vlasov diffusions. Our main result shows that the mean field…
The Schr\"odinger bridge problem seeks the optimal stochastic process that connects two given probability distributions with minimal energy modification. While the Sinkhorn algorithm is widely used to solve the static optimal transport…
This article discusses an optimal control problem for a phase field model of two immiscible incompressible fluid flow, incorporating surface tension effects. The optimal control problem is defined with a $L^2$-cost functional and subject to…
The Lambert problem originated in orbital mechanics. It concerns with determining the initial velocity for a boundary value problem involving the dynamical constraint due to gravitational potential with additional time horizon and endpoint…
Most modern bridge-diffusion methods achieve finite-time transport by specifying an interpolation, Schr\"odinger-bridge, or stochastic-control objective and then learning the associated score or drift field with a neural network. In…
We show convergence of the gradients of the Schr\"odinger potentials to the Brenier map in the small-time limit under general assumptions on the marginals, which allow for unbounded densities and supports. Furthermore, we provide novel…
We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of free-boundary type. The particularity of our approach is that…
The classical Schrodinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time; the likelihood is quantified by the relative entropy between the sought law and…