4 papers
Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing
Konrad Kleinberg, Thomas Kruse
In this paper we provide Monte Carlo and deep neural network approximations for stochastic representations of solutions to linear elliptic partial differential equations with const…
Convexity and strict convexity for compositional neural networks in high-dimensional optimal control
Lars Grüne, Konrad Kleinberg, Thomas Kruse +1
Neural networks (NNs) have emerged as powerful tools for solving high-dimensional optimal control problems. In particular, their compositional structure has been shown to enable ef…
Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality
Arnulf Jentzen, Konrad Kleinberg, Thomas Kruse
Discrete time stochastic optimal control problems and Markov decision processes (MDPs) are fundamental models for sequential decision-making under uncertainty and as such provide t…
Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems
Christian Beck, Arnulf Jentzen, Konrad Kleinberg +1
Discrete time stochastic optimal control problems and Markov decision processes (MDPs), respectively, serve as fundamental models for problems that involve sequential decision maki…