Approximative Policy Iteration for Exit Time Feedback Control Problems Driven by Stochastic Differential Equations using Tensor Train Format
DOI10.1137/20M1372500zbMath1492.93196arXiv2010.04465OpenAlexW3092417881WikidataQ115246873 ScholiaQ115246873MaRDI QIDQ5865245
Konstantin Fackeldey, Leon Sallandt, Reinhold Schneider, Mathias Oster
Publication date: 13 June 2022
Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2010.04465
exit timepolicy iterationvariational Monte CarloKoopman operatortensor trainHamilton-Jacobi-Bellmann (HJB)
Feedback control (93B52) Dynamic programming (90C39) Optimal stochastic control (93E20) Numerical solutions to stochastic differential and integral equations (65C30)
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- Tensor-Train Decomposition
- On the numerical approximation of the Perron-Frobenius and Koopman operator
- Application of variational iteration method for Hamilton-Jacobi-Bellman equations
- Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations
- Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids
- Optimal control of molecular dynamics using Markov state models
- A numerical approach to the infinite horizon problem of deterministic control theory
- Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
- Tensor products of Sobolev-Besov spaces and applications to approximation from the hyperbolic cross
- A direct approach to conformational dynamics based on hybrid Monte Carlo
- Chaos, fractals, and noise: Stochastic aspects of dynamics.
- Perfect cocycles through stochastic differential equations
- Tangent cones to tensor train varieties
- Optimum bounds for the distributions of martingales in Banach spaces
- An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations
- Optimal control: novel directions and applications
- Koopman operator spectrum for random dynamical systems
- Neural networks-based backward scheme for fully nonlinear PDEs
- Solving the Kolmogorov PDE by means of deep learning
- Introduction to the Koopman operator in dynamical systems and control theory
- Variational Monte Carlo -- bridging concepts of machine learning and high-dimensional partial differential equations
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Data-based approximate policy iteration for affine nonlinear continuous-time optimal control design
- Probabilistic max-plus schemes for solving Hamilton-Jacobi-Bellman equations
- On manifolds of tensors of fixed TT-rank
- Controlled Markov processes and viscosity solutions
- On the mathematical foundations of learning
- Generalized Hamilton--Jacobi--Bellman Equations with Dirichlet Boundary Condition and Stochastic Exit Time Optimal Control Problem
- Approximate policy iteration: a survey and some new methods
- The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
- Applied Koopmanism
- Stochastic Optimal Control in Infinite Dimension
- Tensor Spaces and Numerical Tensor Calculus
- Robust shortest path planning and semicontractive dynamic programming
- Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
- FUNCTIONAL EQUATIONS IN THE THEORY OF DYNAMIC PROGRAMMING. V. POSITIVITY AND QUASI-LINEARITY
- On the approximation of curves by line segments using dynamic programming
- Support Vector Machines
- A Generalized dynamic programming principle and hamilton-jacobi-bellman equation
- An Introductory Approach to Duality in Optimal Stochastic Control
- On the Approximation of Complicated Dynamical Behavior
- Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation
- Hamiltonian Systems and Transformation in Hilbert Space
- On the isolated spectrum of the Perron-Frobenius operator
- Parametric PDEs: sparse or low-rank approximations?
- Numerical tensor calculus
- Infinite Horizon Stochastic Optimal Control Problems with Running Maximum Cost
- The Bellman equation for control of the running max of a diffusion and applications to look-back options
- On the Convergence of Finite Element Methods for Hamilton--Jacobi--Bellman Equations
- Optimal weighted least-squares methods
- Solving high-dimensional partial differential equations using deep learning
- Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations
- Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks
- Convergence bounds for empirical nonlinear least-squares
- Stochastic Processes and Applications
- Variational approach to rare event simulation using least-squares regression
- Stochastic Optimal Control of Structures
- Tensor Spaces and Hierarchical Tensor Representations
- Semi-Lagrangian Approximation Schemes for Linear and Hamilton—Jacobi Equations
- Sparse grids
- A fast algorithm for the two dimensional HJB equation of stochastic control
- Numerical solution of the finite horizon stochastic linear quadratic control problem
- Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs
- Stochastic Control Theory
- Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
- Stochastic Equations in Infinite Dimensions
- Stochastic differential equations. An introduction with applications.
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