arXiv research

Researchers develop neural networks for approximating functions in Banach spaces.

FFN addresses spectral bias in neural value approximation, improving reinforcement learning performance.

New method uses extreme value theory to estimate neural network errors.

Complex-valued neural networks can approximate any continuous function.

The problem of explaining the behavior of deep neural networks has recently gained a lot of attention. While several attribution methods have been proposed, most come without strong theoretical foundations, which raises questions about their reliability. On the other hand, the literature on cooperative game theory sugg…

CVNNs improve performance in tasks with complex-valued inputs.

Random feature models approximate functions in Banach spaces efficiently.

Improved singular value approximation for convolutional layers.

Real-world problems of operations research are typically high-dimensional and combinatorial. Linear programs are generally used to formulate and efficiently solve these large decision problems. However, in multi-period decision problems, we must often compute expected downstream values corresponding to current decision…

Sobolev training helps neural nets fit function values and derivatives.

This paper compares linear regression and neural networks for pricing swing options.

Complex-valued neural networks can approximate any continuous function with bounded widths and depths.

Neural operators approximate Stackelberg game solutions.

FVI method calculates bicausal OT with neural networks, outperforming other methods.

Deep neural nets approximate high-dimensional HJB equations efficiently.

Deep networks with path norm regularization can approximate analytic functions.

Deep, wide ConvResNets can approximate functions and their smoothness.

We propose a novel Shapley value approach to help address neural networks' interpretability and "vanishing gradient" problems. Our method is based on an accurate analytical approximation to the Shapley value of a neuron with ReLU activation. This analytical approximation admits a linear propagation of relevance across …

In this paper, we consider the stochastic iterative counterpart of the value iteration scheme wherein only noisy and possibly biased approximations of the Bellman operator are available. We call this counterpart as the approximate value iteration (AVI) scheme. Neural networks are often used as function approximators, i…

Dense neural networks can't approximate all functions.

DFNNs predict non-Euclidean responses from Euclidean predictors.

Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms. Despite its empirical success, the non-asymptotic convergence rate of neural Q-learning remains virtually unknown. In this paper, we present a finite-time analysis of a…

Deep learning approximates Bermudan option exposures and future values.

Proposes EVE for efficient exploration in reinforcement learning.

Neural likelihood approximates integer time series data efficiently.

Neural networks allow Q-learning reinforcement learning agents such as deep Q-networks (DQN) to approximate complex mappings from state spaces to value functions. However, this also brings drawbacks when compared to other function approximators such as tile coding or their generalisations, radial basis functions (RBF) …

LUNO linearizes neural operators to quantify their predictive uncertainty.

Stochastic gradient descent (SGD) has achieved great success in training deep neural network, where the gradient is computed through back-propagation. However, the back-propagated values of different layers vary dramatically. This inconsistence of gradient magnitude across different layers renders optimization of deep …

The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value. These conditional expectations are classically computed by regression techniques o…

New methods improve Fisher Matrix approximations for neural networks at low cost.

This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of neural networks in the spirit of deep reinforcement learning, and then the valu…

Deep Galerkin Method estimates value function for mean-field control problem.

Method uses DNNs to approximate functions with specific asymptotic behavior.

This study shows neural nets can approximate Turing machines with meaningful statistical properties.

Study efficient neural operator learning using variation spaces.

We introduce a novel Deep Reinforcement Learning (DRL) algorithm called Deep Quality-Value (DQV) Learning. DQV uses temporal-difference learning to train a Value neural network and uses this network for training a second Quality-value network that learns to estimate state-action values. We first test DQV's update rules…

Study assesses neural nets for optimization problems, highlighting SiLU's effectiveness.

Reinforcement learning algorithms can solve dynamic decision-making and optimal control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value function and policy mappings. Commonly used numerical approximators, such as ne…

Estimates and convergence of neural network approximations without structural assumptions.

Deep neural networks solve optimal risk sharing problems.

New RL algorithm tackles large state spaces using optimistic function approximation.

Generalizes neural network approximation to infinite-dimensional manifolds and derivatives.

Deep neural networks can solve optimal stopping problems without dimensionality issues.

A method uses neural networks to approximate sampling distributions of test statistics.

We introduce a novel regularization approach for deep learning that incorporates and respects the underlying graphical structure of the neural network. Existing regularization methods often focus on dropping/penalizing weights in a global manner that ignores the connectivity structure of the neural network. We propose …

We propose a time value related decision function to treat a classical option pricing problem raised by Hutchinson-Lo-Poggio. In numerical experiments, the new decision function significantly improves the original model of Hutchinson-Lo-Poggio with faster convergence and better generalization performance. By proving a …

Paper proposes a new optimization framework for learning eigenfunctions of operators.

Study evaluates thresholds for removing noise from DNN weights using random matrix theory.