Search Results for author:
Found 11 papers, 1 papers with code
Gradient descent provably escapes saddle points in the training of shallow ReLU networks
Dynamical systems theory has recently been applied in optimization to prove that gradient descent algorithms avoid so-called strict saddle points of the loss function.
Computation of conditional expectations with guarantees
Theoretically, the conditional expectation of a square-integrable random variable $Y$ given a $d$-dimensional random vector $X$ can be obtained by minimizing the mean squared distance between $Y$ and $f(X)$ over all Borel measurable functions $f \colon \mathbb{R}^d \to \mathbb{R}$.
Assessing asset-liability risk with neural networks
We introduce a neural network approach for assessing the risk of a portfolio of assets and liabilities over a given time period.
Landscape analysis for shallow neural networks: complete classification of critical points for affine target functions
In this paper, we analyze the landscape of the true loss of neural networks with one hidden layer and ReLU, leaky ReLU, or quadratic activation.
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions
This Lyapunov function is the central tool in our convergence proof of the gradient descent method.
Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems
In this article we introduce and study a deep learning based approximation algorithm for solutions of stochastic partial differential equations (SPDEs).
Non-convergence of stochastic gradient descent in the training of deep neural networks
Deep neural networks have successfully been trained in various application areas with stochastic gradient descent.
Pricing and hedging American-style options with deep learning
In this paper we introduce a deep learning method for pricing and hedging American-style options.
Efficient approximation of high-dimensional functions with neural networks
In this paper, we develop a framework for showing that neural networks can overcome the curse of dimensionality in different high-dimensional approximation problems.
Numerical Analysis Numerical Analysis 68T07 I.2.0
Solving high-dimensional optimal stopping problems using deep learning
We present numerical results for a large number of example problems, which include the pricing of many high-dimensional American and Bermudan options, such as Bermudan max-call options in up to 5000 dimensions.
Deep splitting method for parabolic PDEs
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning.
