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In this paper, we aim to develop the theory of optimal stochastic control for branching diffusion processes where both the movement and the reproduction of the particles depend on the control. More precisely, we study the problem of…

Probability · Mathematics 2016-09-19 Julien Claisse

We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a non standard class of switching controls introduced in this paper.…

Probability · Mathematics 2016-07-04 Erhan Bayraktar , Andrea Cosso , Huyen Pham

We introduce a stochastic version of the optimal transport problem. We provide an analysis by means of the study of the associated Hamilton-Jacobi-Bellman equation, which is set on the set of probability measures. We introduce a new…

Analysis of PDEs · Mathematics 2024-05-22 Charles Bertucci

This paper introduces the formalism required to analyze a certain class of stochastic control problems that involve a super diffusion as the underlying controlled system. To establish the existence of these processes, we show that they are…

Probability · Mathematics 2024-11-19 Antonio Ocello

We exhibit optimal control strategies for a simple toy problem in which the underlying dynamics depend on a parameter that is initially unknown and must be learned. We consider a cost function posed over a finite time interval, in contrast…

Optimization and Control · Mathematics 2020-02-27 Charles L. Fefferman , Bernat Guillen Pegueroles , Clarence W. Rowley , Melanie Weber

We consider the computation of free energy-like quantities for diffusions in high dimension, when resorting to Monte Carlo simulation is necessary. Such stochastic computations typically suffer from high variance, in particular in a low…

Numerical Analysis · Mathematics 2023-07-06 Grégoire Ferré

In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic differential equations. We…

Optimization and Control · Mathematics 2022-12-26 Jianjun Zhou

We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in [4], we prove a corresponding randomized dynamic programming principle (DPP) for the value function, which is…

Probability · Mathematics 2016-09-12 Elena Bandini , Andrea Cosso , Marco Fuhrman , Huyên Pham

In this note, we demonstrate that a locally semiconvex viscosity supersolution to a possibly degenerate fully nonlinear elliptic Hamilton-Jacobi-Bellman (HJB) equation is differentiable along the directions spanned by the range of the…

Optimization and Control · Mathematics 2025-01-28 Salvatore Federico , Giorgio Ferrari , Mauro Rosestolato

We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents,…

Probability · Mathematics 2023-01-10 Joe Jackson , Daniel Lacker

In this paper, we consider a stochastic decision problem for a system governed by a stochastic differential equation, in which an optimal decision is made in such a way to minimize a vector-valued accumulated cost over a finite-time horizon…

Optimization and Control · Mathematics 2018-01-08 Getachew K. Befekadu

The interplay between stochastic processes and optimal control has been extensively explored in the literature. With the recent surge in the use of diffusion models, stochastic processes have increasingly been applied to sample generation.…

Machine Learning · Computer Science 2024-10-10 Tingwei Meng , Zongren Zou , Jérôme Darbon , George Em Karniadakis

We consider long term average or `ergodic' optimal control poblems with a special structure: Control is exerted in all directions and the control costs are proportional to the square of the norm of the control field with respect to the…

Optimization and Control · Mathematics 2016-02-01 Joris Bierkens , Vladimir Y. Chernyak , Michael Chertkov , Hilbert J. Kappen

We study a stochastic optimal control problem for fully coupled forward-backward stochastic control systems with a nonempty control domain. For our problem, the first-order and second-order variational equations are fully coupled linear…

Optimization and Control · Mathematics 2018-12-05 Mingshang Hu , Shaolin Ji , Xiaole Xue

The paper is devoted to a stochastic optimal control problem for a two scale, infinite dimensional, stochastic system. The state of the system consists of slow and fast component and its evolution is driven by both continuous Wiener noises…

Optimization and Control · Mathematics 2024-01-17 Elena Bandini , Giuseppina Guatteri , Gianmario Tessitore

This paper presents a novel methodology to tackle feedback optimal control problems in scenarios where the exact state of the controlled process is unknown. It integrates data assimilation techniques and optimal control solvers to manage…

Optimization and Control · Mathematics 2024-04-10 Siming Liang , Ruoyu Hu , Feng Bao , Richard Archibald , Guannan Zhang

This paper, which is the natural continuation of a previous paper by the same authors, studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes…

Optimization and Control · Mathematics 2009-07-10 Salvatore Federico , Ben Goldys , Fausto Gozzi

The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…

Optimization and Control · Mathematics 2015-12-01 Tan H. Cao , Boris S. Mordukhovich

We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems…

Optimization and Control · Mathematics 2025-03-07 Andrea Cosso , Laura Perelli

In this paper we are interested in a new type of {\it mean-field}, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths…

Probability · Mathematics 2017-02-21 Rainer Buckdahn , Juan Li , Jin Ma