Related papers: A McKean-Pontrygin maximum principle for entropic-…
We introduce a stochastic optimal transport for the Langevin dynamics with positive mass and study its zero--mass limit. The new aspect of this paper is that we only fix the initial and terminal probability distributions of the positions of…
In this study, we consider an optimal control problem driven by a stochastic differential system with a stopping time terminal cost functional. We establish the stochastic maximum principle for this new kind of an optimal control problem by…
We develop a general approach to prove global regularity estimates for quadratic optimal transport using the entropic regularisation of the problem and the Prekopa-Leindler inequality.
Motivated by a problem posed by Aldous, our goal is to find the maximal-entropy win-martingale: In a sports game between two teams, the chance the home team wins is initially $x_0 \in (0,1)$ and finally 0 or 1. As an idealization we take a…
The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the…
In the context of mean field games, with possible control of the diffusion coefficient, we consider a path-dependent version of the planning problem introduced by P.L. Lions: given a pair of marginal distributions $(\mu_0, \mu_1)$, find a…
In this paper we give a new approach to introduce switching strategies in a special class of optimal multiprocesses. Defined as the set of partitions of the time interval, switching strategies become the character of a classical control.…
In this paper, we study an optimal control problem of a mean-field forward-backward stochastic system with random jumps in progressive structure, where both regular and singular controls are considered in our formula. In virtue of the…
This paper addresses the Optimal Transport problem, which is regularized by the square of Euclidean $\ell_2$-norm. It offers theoretical guarantees regarding the iteration complexities of the Sinkhorn--Knopp algorithm, Accelerated Gradient…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
A general stochastic maximum principle is proved for optimal controls of semilinear stochastic evolution equations. Stochastic evolution operators, and the control with values in a general set enter into both drift and diffusion terms.
We shall consider a stochastic maximum principle of optimal control for a control problem associated with a stochastic partial differential equations of the following type: d x(t) = (A(t) x(t) + a (t, u(t)) x(t) + b(t, u(t)) dt +…
We consider the free endpoint Mayer problem for a controlled Moreau process, the control acting as a perturbation of the dynamics driven by the normal cone, and derive necessary optimality conditions of Pontryagin's Maximum Principle type.…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
In this paper, we propose the optimal production transport model, which is an extension of the classical optimal transport model. We observe in economics, the production of the factories can always be adjusted within a certain range, while…
Conditional McKean-Vlasov control problems involve controlling McKean-Vlasov diffusions where the interaction occurs through the law of the state process conditionally on it staying in a domain. Introduced by Lions in his 2016 lectures at…
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the…
We take a new look at the relation between the optimal transport problem and the Schr\"{o}dinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing…
We introduce a class of maximum-entropy states that naturally includes within it all of the major continuous-time stochastic processes that have been applied to animal movement, including Brownian motion, Ornstein-Uhlenbeck motion,…