Related papers: Generative optimal transport via forward-backward …
We solve explicitly a two-dimensional singular control problem of finite fuel type for infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price…
We study a class of controlled rough differential equations. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the…
The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…
Optimal control and the associated second-order path-dependent Hamilton-Jacobi-Bellman (PHJB) equation are studied for unbounded functional stochastic evolution systems in Hilbert spaces. The notion of viscosity solution without…
Viewing stochastic processes through the lens of occupation measures has proved to be a powerful angle of attack for the theoretical and computational analysis of stochastic optimal control problems. We present a simple modification of the…
We consider a Bayesian adaptive optimal stochastic control problem where a hidden static signal has a non-separable influence on the drift of a noisy observation. Being allowed to control the specific form of this dependence, we aim at…
In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss due to the mismatch between the true model…
We consider transport over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with certain initial and final marginals.…
We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are…
This paper investigates a class of multiscale stochastic control problems driven by $\alpha$-stable L\'evy noises, where the controlled dynamics evolve across separate slow and fast time scales. The associated value functions are governed…
Population dynamics is the study of temporal and spatial variation in the size of populations of organisms and is a major part of population ecology. One of the main difficulties in analyzing population dynamics is that we can only obtain…
Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…
Transferring a physical system from an initial to a final state while minimizing energetic losses is an interdisciplinary control problem that bridges stochastic thermodynamics and optimal transport theory. Recent research typically…
This paper presents a novel approach for steering the state of a stochastic control-affine system to a desired target within a finite time horizon. Our method leverages the time-reversal of diffusion processes to construct the required…
Many complex real world phenomena exhibit abrupt, intermittent or jumping behaviors, which are more suitable to be described by stochastic differential equations under non-Gaussian L\'evy noise. Among these complex phenomena, the most…
We deal with an infinite horizon, infinite dimensional stochastic optimal control problem arising in the study of economic growth in time-space. Such problem has been the object of various papers in deterministic cases when the possible…
We study a discounted singular stochastic control problem driven by a general L\'evy process, where the objective is to minimize a cost functional composed of a running cost and a control cost that depends on the current state of the…
The entropy regularization is inspired by information entropy from machine learning and the ideas of exploration and exploitation in reinforcement learning, which appears in the control problem to design an approximating algorithm for the…
In this paper, we study a class of stochastic optimal control problem with jumps under partial information. More precisely, the controlled systems are described by a fully coupled nonlinear multi- dimensional forward-backward stochastic…
We treat infinite horizon optimal control problems by solving the associated stationary Hamilton-Jacobi-Bellman (HJB) equation numerically to compute the value function and an optimal feedback law. The dynamical systems under consideration…