Related papers: Research on Optimal Control Problem Based on Reinf…
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…
We consider reinforcement learning (RL) in continuous time and study the problem of achieving the best trade-off between exploration of a black box environment and exploitation of current knowledge. We propose an entropy-regularized reward…
Maximum entropy reinforcement learning (RL) methods have been successfully applied to a range of challenging sequential decision-making and control tasks. However, most of existing techniques are designed for discrete-time systems. As a…
This work provides a rigorous framework for studying continuous time control problems in uncertain environments. The framework considered models uncertainty in state dynamics as a measure on the space of functions. This measure is…
This paper studies the continuous-time reinforcement learning (RL) for optimal switching problems across multiple regimes. We consider a type of exploratory formulation under entropy regularization where the agent randomizes both the timing…
In this paper, we study the optimal stopping problem in the so-called exploratory framework, in which the agent takes actions randomly conditioning on current state and an entropy-regularized term is added to the reward functional. Such a…
We study the discrete-time linear-quadratic (LQ) control model using reinforcement learning (RL). Using entropy to measure the cost of exploration, we prove that the optimal feedback policy for the problem must be Gaussian type. Then, we…
This work uses the entropy-regularised relaxed stochastic control perspective as a principled framework for designing reinforcement learning (RL) algorithms. Herein agent interacts with the environment by generating noisy controls…
We study the problem of generating control laws for systems with unknown dynamics. Our approach is to represent the controller and the value function with neural networks, and to train them using loss functions adapted from the…
In this note, we study a class of indefinite stochastic McKean-Vlasov linear-quadratic (LQ in short) control problem under the control taking nonnegative values. In contrast to the conventional issue, both the classical dynamic programming…
In this paper, we present a novel method for computing the optimal feedback gain of the infinite-horizon Linear Quadratic Regulator (LQR) problem via an ordinary differential equation. We introduce a novel continuous-time Bellman error,…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
This paper studies optimal consensus tracking problem of heterogeneous linear multi-agent systems. By introducing tracking error dynamics, the optimal tracking problem is reformulated as finding a Nash-equilibrium solution of a multi-player…
We address the crucial yet underexplored stability properties of the Hamilton--Jacobi--Bellman (HJB) equation in model-free reinforcement learning contexts, specifically for Lipschitz continuous optimal control problems. We bridge the gap…
Commonly in reinforcement learning (RL), rewards are discounted over time using an exponential function to model time preference, thereby bounding the expected long-term reward. In contrast, in economics and psychology, it has been shown…
In this paper, we study a time-inconsistent stochastic optimal control problem with a recursive cost functional by a multi-person hierarchical differential game approach. An equilibrium strategy of this problem is constructed and a…
In this paper, we propose Q-learning algorithms for continuous-time deterministic optimal control problems with Lipschitz continuous controls. Our method is based on a new class of Hamilton-Jacobi-Bellman (HJB) equations derived from…
The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the…
In this paper, we will deal with a Linear Quadratic Optimal Control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability…
Optimal feedback control with implicit Hamiltonians poses a fundamental challenge for learning-based value function methods due to the absence of closed-form optimal control laws. Recent work~\cite{gelphman2025end} introduced an implicit…