Related papers: Value-Gradient based Formulation of Optimal Contro…
In this paper, we study an optimal control problem of linear backward stochastic differential equation (BSDE) with quadratic cost functional under partial information. This problem is solved completely and explicitly by using a stochastic…
This paper addresses the model-free nonlinear optimal problem with generalized cost functional, and a data-based reinforcement learning technique is developed. It is known that the nonlinear optimal control problem relies on the solution of…
We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows…
Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice this normally means optimizing the value of some observable, a so…
This work investigates the optimal control problem for reflected McKean-Vlasov SDEs and the viscosity solutions to Hamilton-Jacobi-Bellman(HJB) equations on the Wasserstein space in terms of intrinsic derivative. It follows from the flow…
In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we…
Option contracts on two underlying assets within uncertain volatility models have their worst-case and best-case prices determined by a two-dimensional (2D) Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) with…
Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild…
This paper proposes two algorithms for solving stochastic control problems with deep learning, with a focus on the utility maximisation problem. The first algorithm solves Markovian problems via the Hamilton Jacobi Bellman (HJB) equation.…
We study optimal stochastic control problem for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients, and gain functionals are path-dependent, and importantly we do not make any ellipticity…
We consider a Bolza-type optimal control problem for a dynamical system described by a fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1)$. The value of this problem is introduced as a functional in a…
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…
In this paper, a novel optimal control-based baseline function is presented for the policy gradient method in deep reinforcement learning (RL). The baseline is obtained by computing the value function of an optimal control problem, which is…
We consider policy gradient methods for stochastic optimal control problem in continuous time. In particular, we analyze the gradient flow for the control, viewed as a continuous time limit of the policy gradient method. We prove the global…
This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a…
We study an optimal control problem on infinite time horizon with semimartingale strategies, random coefficients and regime switching. The value function and the optimal strategy can be characterized in terms of three systems of backward…
The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of…
A new method for the optimal solutions is proposed. Originating from the continuous-time dynamics stability theory in the control field, the optimal solution is anticipated to be obtained in an asymptotically evolving way. By introducing a…
The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems…
Model-based reinforcement learning techniques accelerate the learning task by employing a transition model to make predictions. In this paper, a model-based learning approach is presented that iteratively computes the optimal value function…