Related papers: A kernel-based method for Schr\"odinger bridges
We consider a general class of mean field control problems described by stochastic delayed differential equations of McKean-Vlasov type. Two numerical algorithms are provided based on deep learning techniques, one is to directly…
The Mean-Field Schrodinger Bridge (MFSB) problem is an optimization problem aiming to find the minimum effort control policy to drive a McKean-Vlassov stochastic differential equation from one probability measure to another. In the context…
This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are…
Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…
How to steer a given joint state probability density function to another over finite horizon subject to a controlled stochastic dynamics with hard state (sample path) constraints? In applications, state constraints may encode safety…
We study the subclass of potential mean-field games in which the running interaction cost and the terminal target cost are both expressed through reproducing-kernel maximum mean discrepancy (MMD) penalties, and develop a computational…
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…
This paper is concerned with the numerical integration of stochastic differential equations (SDEs) which govern diffusion processes driven by a standard Wiener process. With the latter being replaced by a sequence of increments at discrete…
We study the optimal control formulation for stochastic nonlinear Schrodinger equation (SNLSE) on a finite graph. By viewing the SNLSE as a stochastic Wasserstein Hamiltonian flow on density manifold, we show the global existence of a…
We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In the case of multiplicative noise, existence of optimal controls and necessary conditions for optimality are derived. In…
We consider the problem of sampling transition paths between two given metastable states of a molecular system, e.g. a folded and unfolded protein or products and reactants of a chemical reaction. Due to the existence of high energy…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…
We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model free, non-parametric…
Exploiting a fluid dynamic formulation for which a probabilistic counterpart might not be available, we extend the theory of Schroedinger bridges to the case of inertial particles with losses and general, possibly singular diffusion…
Complex systems can be effectively modeled via graphs that encode networked interactions, where relations between entities or nodes are often quantified by signed edge weights, e.g., promotion/inhibition in gene regulatory networks, or…
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…
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained…
Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…
In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a…
We address the problem of Schr\"odinger potential estimation, which plays a crucial role in modern generative modelling approaches based on Schr\"odinger bridges and stochastic optimal control for SDEs. Given a simple prior diffusion…