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For a general entropy-regularized stochastic control problem on an infinite horizon, we prove that a policy iteration algorithm (PIA) converges to an optimal relaxed control. Contrary to the standard stochastic control literature, classical…
In this paper, a stochastic control problem under model uncertainty with general penalty term is studied. Two types of penalties are considered. The first one is of type f-divergence penalty treated in the general framework of a continuous…
Data-Enabled Predictive Control (DeePC) bypasses the need for system identification by directly leveraging raw data to formulate optimal control policies. However, the size of the optimization problem in DeePC grows linearly with respect to…
In this paper, we consider optimal control of stochastic differential equations subject to an expected path constraint. The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs. In…
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…
We study the optimal dividend problem for a firm's manager who has partial information on the profitability of the firm. The problem is formulated as one of singular stochastic control with partial information on the drift of the underlying…
In this note, we consider infinite horizon optimal control problems with deterministic systems. Since exact solutions to these problems are often intractable, we propose a parallel model predictive control (MPC) method that provides an…
We present and analyze a new method for solving optimal control problems for Volterra integral equations, based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential…
We consider solution of stochastic storage problems through regression Monte Carlo (RMC) methods. Taking a statistical learning perspective, we develop the dynamic emulation algorithm (DEA) that unifies the different existing approaches in…
In this paper, as a first step in examining the properties of a feasible portfolio subset that is characterized by budget and risk constraints, we assess the maximum and minimum of the investment concentration using replica analysis. To do…
This work presents the solution to a class of decentralized linear quadratic state-feedback control problems, in which the plant and controller must satisfy the same combination of delay and sparsity constraints. Using a novel decomposition…
This paper focuses on the discrete-time backward stochastic linear quadratic (BSLQ) optimal control problem with nonhomogeneous system terms and cost function cross terms. The terminal constraint of such systems distinguishes it from…
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…
Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a…
We develop a Monte-Carlo based numerical method for solving discrete-time stochastic optimal control problems with inventory. These are optimal control problems in which the control affects only a deterministically evolving inventory…
Optimal and safety-critical control are fundamental problems for stochastic systems, and are widely considered in real-world scenarios such as robotic manipulation and autonomous driving. In this paper, we consider the problem of…
We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal control problems subject to parabolic partial differential equation (PDE) constraints under uncertainty: the state in our setting is the solution of…
This paper is concerned with the designing, analyzing and implementing linear and nonlinear discretization scheme for the distributed optimal control problem (OCP) with the Cahn-Hilliard (CH) equation as constrained. We propose three…
We consider de Finetti's optimal dividends problem with absolutely continuous strategies in a spectrally negative L\'evy model with Parisian ruin as the termination time. The problem considered is essentially a generalization of both the…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…