Related papers: The Relationship between Maximum Principle and Dyn…
This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential…
In this paper we study the optimal stochastic control problem for a path-dependent stochastic system under a recursive path-dependent cost functional, whose associated Bellman equation from dynamic programming principle is a path-dependent…
We study the problem of optimal portfolio selection under stochastic volatility within a continuous time reinforcement learning framework with portfolio constraints. Exploration is modeled through entropy-regularized relaxed controls, where…
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…
Considering that the decision-making environment faced by reinforcement learning (RL) agents is full of Knightian uncertainty, this paper describes the exploratory state dynamics equation in Knightian uncertainty to study the…
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…
In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…
In this paper, we present a novel maximum entropy formulation of the Differential Dynamic Programming algorithm and derive two variants using unimodal and multimodal value functions parameterizations. By combining the maximum entropy…
In this paper, we consider the problem of controlling a diffusion process pertaining to an opioid epidemic dynamical model with random perturbation so as to prevent it from leaving a given bounded open domain. Here, we assume that the…
In this article, we provide a numerical method based on fitted finite volume method to approximate the Hamilton-Jacobi-Bellman (HJB) equation coming from stochastic optimal control problems. The computational challenge is due to the nature…
This paper examines the stochastic maximum principle (SMP) for a forward-backward stochastic control system where the backward state equation is characterized by the backward stochastic differential equation (BSDE) with quadratic growth and…
A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and…
In this paper we present a novel sampling-based numerical scheme designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear…
We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton-Jacobi-Bellman equation usually calls for…
This paper proposes a method to design an optimal dynamic contract between a principal and an agent, who has the authority to control both the principal's revenue and an engineered system. The key characteristic of our problem setting is…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
When randomness in demand affects the sales of a product, retailers use dynamic pricing strategies to maximize their profits. In this article, we formulate the pricing problem as a continuous-time stochastic optimal control problem and find…
This paper studies mean-field control problems with state-control joint law dependence and Poissonian common noise. We develop the stochastic maximum principle (SMP) and establish its connection to the Hamiltonian-Jacobi-Bellman (HJB)…
A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing…
We provide a unifying approximate dynamic programming framework that applies to a broad variety of problems involving sequential estimation. We consider first the construction of surrogate cost functions for the purposes of optimization,…