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This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
With the growing global emphasis on sustainability and the implementation of contemporary environmental policies, photovoltaic (PV) generation is playing an increasingly important role in modern power systems, while its intrinsic…
We propose a physics-informed neural networks (PINNs) framework to solve the infinite-horizon optimal control problem of nonlinear systems. In particular, since PINNs are generally able to solve a class of partial differential equations…
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…
We propose a neural network approach that yields approximate solutions for high-dimensional optimal control problems and demonstrate its effectiveness using examples from multi-agent path finding. Our approach yields controls in a feedback…
A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The method combines a tensor train approximation…
Physics-informed neural solvers offer a promising route to model-based reinforcement learning in continuous time, where optimal feedback synthesis is governed by Hamilton--Jacobi--Bellman (HJB) equations. Practical implementations often…
In this paper, a stochastic optimal control problem is investigated in which the system is governed by a stochastic functional differential equation. In the framework of functional It\^o calculus, we build the dynamic programming principle…
We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this…
One of the core problems in mean-field control and mean-field games is to solve the corresponding McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). Most existing methods are tailored to special cases in which the…
We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential…
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…
Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function…
We study the problem of learning the optimal control policy for fine-tuning a given diffusion process, using general value function approximation. We develop a new class of algorithms by solving a variational inequality problem based on the…
This paper is devoted to a stochastic differential game of functional forward-backward stochastic differential equation (FBSDE, for short). The associated upper and lower value functions of the stochastic differential game are defined by…
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…
In this paper an optimal control problem for a large system of interacting agents is considered using a kinetic perspective. As a prototype model we analyze a microscopic model of opinion formation under constraints. For this problem a…
In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraints for the cost function where the cost function is described by the solution of one reflected backward stochastic differential…