Function Approximation

Function approximation aims to represent complex, potentially high-dimensional functions using simpler, computationally tractable models. Current research emphasizes developing novel architectures, such as Kolmogorov-Arnold networks and those incorporating Chebyshev polynomials or path signatures, alongside improved algorithms like those based on optimism principles or two-timescale methods. These advancements are crucial for addressing challenges in diverse fields, including reinforcement learning, contextual bandits, and scientific machine learning, where accurate and efficient function representation is essential for effective modeling and prediction.

Papers

October 21, 2024

Statistical Inference for Temporal Difference Learning with Linear Function Approximation
Weichen Wu, Gen Li, Yuting Wei, Alessandro Rinaldo
Reinforcement Learning Markov Decision Process Function Approximation Temporal Difference Learning Linear Ordered Data Statistical Inference High Probability Convergence

October 17, 2024

Federated scientific machine learning for approximating functions and solving differential equations with data heterogeneity
Handi Zhang, Langchen Liu, Lu Lu
Physic Informed Neural Network Partial Differential Equation Data Heterogeneity Differential Equation Function Approximation

October 8, 2024

Covering Numbers for Deep ReLU Networks with Applications to Function Approximation and Nonparametric Regression
Weigutian Ou, Helmut Bölcskei
Financial Application Deep Network Average Approximation ReLU Network Sparse Network Function Approximation Nonparametric Regression Deep ReLU Network Better Approximation

October 4, 2024

P1-KAN an effective Kolmogorov Arnold Network for function approximation
Xavier Warin
Multi Layer Kolmogorov Arnold Network High Dimension Function Approximation

October 2, 2024

On Expressive Power of Looped Transformers: Theoretical Analysis and Enhancement via Timestep Encoding
Kevin Xu, Issei Sato
Feature Enhancement Theoretical Analysis Function Approximation Expressive Power Approximation Rate Temporal Encoding

September 27, 2024

Chebyshev Feature Neural Network for Accurate Function Approximation
Zhongshu Xu, Yuan Chen, Dongbin Xiu
Function Approximation Hidden Layer Frequency Learning

September 24, 2024

Second Order Bounds for Contextual Bandits with Function Approximation
Aldo Pacchiano
Contextual Bandit Regret Bound Function Approximation Regret Algorithm

August 21, 2024

Networked Communication for Mean-Field Games with Function Approximation and Empirical Mean-Field Estimation
Patrick Benjamin, Alessandro Abate
Network Programming Mean Field Function Approximation Mean Field Game Decentralized Agent

August 14, 2024

Adaptive Basis Function Selection for Computationally Efficient Predictions
Anton Kullberg, Frida Viset, Isaac Skog, Gustaf Hendeby
Gaussian Process Function Approximation Prediction Accuracy Basis Function Efficient Prediction

August 13, 2024

Heavy-Ball Momentum Accelerated Actor-Critic With Function Approximation
Yanjie Dong, Haijun Zhang, Gang Wang, Shisheng Cui, Xiping Hu
Markov Decision Process Function Approximation Reinforcement Learning Task Critic Model Heavy Ball Stochastic Policy Gradient

July 23, 2024

How Can Deep Neural Networks Fail Even With Global Optima?
Qingguang Guan
Deep Neural Network Function Approximation Shallow Neural Network ReLU Layer Global Optimum

July 17, 2024

A Survey on Universal Approximation Theorems
Midhun T Augustine
Neural Network Timely Survey Universal Approximation Function Approximation Theorem Driven Question Approximation Capability

July 8, 2024

On Bellman equations for continuous-time policy evaluation I: discretization and approximation
Wenlong Mou, Yuhua Zhu
Reinforcement Learning Diffusion Model Average Approximation Function Approximation Data Discretization Bellman Equation Continuous Time Trajectory

July 2, 2024

Equidistribution-based training of Free Knot Splines and ReLU Neural Networks
Simone Appella, Simon Arridge, Chris Budd, Teo Deveney, Lisa Maria Kreusser
Function Approximation Shallow Neural Network Rectified Linear Unit Training Data Distribution

June 25, 2024

SigKAN: Signature-Weighted Kolmogorov-Arnold Networks for Time Series
Hugo Inzirillo, Remi Genet
Time Series Kolmogorov Arnold Network Function Approximation Dimensional Approximation Path Signature

May 31, 2024

Target Networks and Over-parameterization Stabilize Off-policy Bootstrapping with Function Approximation
Fengdi Che, Chenjun Xiao, Jincheng Mei, Bo Dai, Ramki Gummadi, Oscar A Ramirez, Christopher K Harris, A. Rupam Mahmood, Dale Schuurmans
Function Approximation Episodic Markov Decision Process Bootstrapping End to End Goal Node Trajectory Truncation

May 19, 2024

Approximation and Gradient Descent Training with Neural Networks
G. Welper
Neural Network Gradient Descent Gradient Flow Average Approximation Neural Tangent Kernel Function Approximation Benign Over Parameterization

May 12, 2024

Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation
Sidharth SS, Keerthana AR, Gokul R, Anas KP
High Dimensional Kolmogorov Arnold Network Function Approximation Efficient Architecture Learned Function Chebyshev Davidson Algorithm Nonlinear Function Approximation

April 17, 2024

Function Approximation for Reinforcement Learning Controller for Energy from Spread Waves
Soumyendu Sarkar, Vineet Gundecha, Sahand Ghorbanpour, Alexander Shmakov, Ashwin Ramesh Babu, Avisek Naug, Alexandre Pichard, Mathieu Cocho
Reinforcement Learning Multi Agent Reinforcement Learning Function Approximation Energy Policy Research Spread Wave Wave Energy Converter

March 17, 2024

Prior-dependent analysis of posterior sampling reinforcement learning with function approximation
Yingru Li, Zhi-Quan Luo
Reinforcement Learning Function Approximation Model Based Prior Bayesian Regret Linear Mixture Markov Decision Process Prior Dependent

Function Approximation

Papers

Statistical Inference for Temporal Difference Learning with Linear Function Approximation

Federated scientific machine learning for approximating functions and solving differential equations with data heterogeneity

Covering Numbers for Deep ReLU Networks with Applications to Function Approximation and Nonparametric Regression

P1-KAN an effective Kolmogorov Arnold Network for function approximation

On Expressive Power of Looped Transformers: Theoretical Analysis and Enhancement via Timestep Encoding

Chebyshev Feature Neural Network for Accurate Function Approximation

Second Order Bounds for Contextual Bandits with Function Approximation

Networked Communication for Mean-Field Games with Function Approximation and Empirical Mean-Field Estimation

Adaptive Basis Function Selection for Computationally Efficient Predictions

Heavy-Ball Momentum Accelerated Actor-Critic With Function Approximation

How Can Deep Neural Networks Fail Even With Global Optima?

A Survey on Universal Approximation Theorems

On Bellman equations for continuous-time policy evaluation I: discretization and approximation

Equidistribution-based training of Free Knot Splines and ReLU Neural Networks

SigKAN: Signature-Weighted Kolmogorov-Arnold Networks for Time Series

Target Networks and Over-parameterization Stabilize Off-policy Bootstrapping with Function Approximation

Approximation and Gradient Descent Training with Neural Networks

Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation

Function Approximation for Reinforcement Learning Controller for Energy from Spread Waves

Prior-dependent analysis of posterior sampling reinforcement learning with function approximation