Related papers: Stabilized neural Hamilton--Jacobi--Bellman solver…
Control barrier functions (CBFs) have been demonstrated as an effective method for safety-critical control of autonomous systems. Although CBFs are simple to deploy, their design remains challenging, motivating the development of…
This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution…
This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic…
A gradient-enhanced functional tensor train cross approximation method for the resolution of the Hamilton-Jacobi-Bellman (HJB) equations associated to optimal feedback control of nonlinear dynamics is presented. The procedure uses samples…
This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity. The neural SDEs with $N$ samples can be linked to the $N$-particle…
Physics-informed deep learning models have emerged as powerful tools for learning dynamical systems. These models directly encode physical principles into network architectures. However, systematic benchmarking of these approaches across…
This paper first introduces a method to approximate the value function of high-dimensional optimal control by neural networks. Based on the established relationship between Pontryagin's maximum principle (PMP) and the value function of the…
Reinforcement learning (RL) excels in applications such as video games, but ensuring safety as well as the ability to achieve the specified goals remains challenging when using RL for real-world problems, such as human-aligned tasks where…
Using the policy gradient algorithm, we train a single-hidden-layer neural network to balance a physically accurate simulation of a single inverted pendulum. The trained weights and biases can then be transferred to a physical agent, where…
Recent developments in autonomous driving and robotics underscore the necessity of safety-critical controllers. Control barrier functions (CBFs) are a popular method for appending safety guarantees to a general control framework, but they…
This work presents a hybrid modeling approach to data-driven learning and representation of unknown physical processes and closure parameterizations. These hybrid models are suitable for situations where the mechanistic description of…
Real-world reinforcement learning is often \emph{nonstationary}: rewards and dynamics drift, accelerate, oscillate, and trigger abrupt switches in the optimal action. Existing theory often represents nonstationarity with coarse-scale models…
We investigate robust model-free reinforcement learning algorithms designed for environments that may be dynamic or even adversarial. Traditional state-based policies often struggle to accommodate the challenges imposed by the presence of…
We introduce a novel extension to robust control theory that explicitly addresses uncertainty in the value function's gradient, a form of uncertainty endemic to applications like reinforcement learning where value functions are…
In deterministic systems, reinforcement learning-based online approximate optimal control methods typically require a restrictive persistence of excitation (PE) condition for convergence. This paper presents a concurrent learning-based…
We consider a time-consistent mean-variance portfolio selection problem of an insurer and allow for the incorporation of basis (mortality) risk. The optimal solution is identified with a Nash subgame perfect equilibrium. We characterize an…
We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems…
An advantageous feature of piecewise constant policy timestepping for Hamilton-Jacobi-Bellman (HJB) equations is that different linear approximation schemes, and indeed different meshes, can be used for the resulting linear equations for…
Hybrid dynamical systems with nonlinear dynamics are one of the most general modeling tools for representing robotic systems, especially contact-rich systems. However, providing guarantees regarding the safety or performance of nonlinear…
We address two major challenges in scientific machine learning (SciML): interpretability and computational efficiency. We increase the interpretability of certain learning processes by establishing a new theoretical connection between…