相关论文: A Novel Policy Iteration Algorithm for Nonlinear C…

The Dynamic Programming approach allows to compute a feedback control for nonlinear problems, but suffers from the curse of dimensionality. The computation of the control relies on the resolution of a nonlinear PDE, the…

Hierarchical reinforcement learning is a promising approach to tackle long-horizon decision-making problems with sparse rewards. Unfortunately, most methods still decouple the lower-level skill acquisition process and the training of a…

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…

Despite its popularity in the reinforcement learning community, a provably convergent policy gradient method for continuous space-time control problems with nonlinear state dynamics has been elusive. This paper proposes proximal gradient…

Many optimal control problems are formulated as two point boundary value problems (TPBVPs) with conditions of optimality derived from the Hamilton-Jacobi-Bellman (HJB) equations. In most cases, it is challenging to solve HJBs due to the…

This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…

A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The method combines a tensor train approximation…

Safety is the priority concern when applying reinforcement learning (RL) algorithms to real-world control problems. While policy iteration provides a fundamental algorithm for standard RL, an analogous theoretical algorithm for safe RL…

A deep learning approach for the approximation of the Hamilton-Jacobi-Bellman partial differential equation (HJB PDE) associated to the Nonlinear Quadratic Regulator (NLQR) problem. A state-dependent Riccati equation control law is first…

The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal…

Power iteration has been generalized to solve many interesting problems in machine learning and statistics. Despite its striking success, theoretical understanding of when and how such an algorithm enjoys good convergence property is…

The goal of this thesis is to provide efficient and provably convergent numerical methods for solving partial differential equations (PDEs) coming from impulse control problems motivated by finance. Impulses, which are controlled jumps in a…

We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on Policy Search algorithms, that compute an approximately optimal policy by following the standard Policy Iteration (PI)…

We consider inexact policy iteration methods for large-scale infinite-horizon discounted MDPs with finite spaces, a variant of policy iteration where the policy evaluation step is implemented inexactly using an iterative solver for linear…

It is well known that time dependent Hamilton-Jacobi-Isaacs partial differential equations (HJ PDE), play an important role in analyzing continuous dynamic games and control theory problems. An important tool for such problems when they…

Reinforcement learning provides a framework for learning control policies that can reproduce diverse motions for simulated characters. However, such policies often exploit unnatural high-frequency signals that are unachievable by humans or…

In this paper, we study policy evaluation in continuous-time reinforcement learning (RL), where the state follows an unknown stochastic differential equation (SDE), but only discrete-time data are available. We first highlight that the…

In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalisation error for a class of penalty terms, and we…

The rising growth of deep neural networks (DNNs) and datasets in size motivates the need for efficient solutions for simultaneous model selection and training. Many methods for hyperparameter optimization (HPO) of iterative learners,…

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…