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

July 1, 2023

A Constructive Approach to Function Realization by Neural Stochastic Differential Equations
Tanya Veeravalli, Maxim Raginsky
Constructive Approach Function Approximation Interacting System Neural Stochastic Differential Equation Neural SDEs Efficient Realization Neural Network Dynamic

June 26, 2023

Effective Minkowski Dimension of Deep Nonparametric Regression: Function Approximation and Statistical Theories
Zixuan Zhang, Minshuo Chen, Mengdi Wang, Wenjing Liao, Tuo Zhao
Low Dimensional Manifold Function Approximation Statistical Model Intrinsic Dimension Effective Dimension Deep Nonparametric

June 12, 2023

Tackling Heavy-Tailed Rewards in Reinforcement Learning with Function Approximation: Minimax Optimal and Instance-Dependent Regret Bounds
Jiayi Huang, Han Zhong, Liwei Wang, Lin F. Yang
Reinforcement Learning Linear Bandit Linear Function Approximation Function Approximation Heavy Tailed Minimax Optimality Instance Dependent Regret Heavy Tailed Noise Heavy Tailed Reward

May 24, 2023

Decision-Aware Actor-Critic with Function Approximation and Theoretical Guarantees
Sharan Vaswani, Amirreza Kazemi, Reza Babanezhad, Nicolas Le Roux
Reinforcement Learning Policy Gradient Function Approximation Theoretical Guarantee Policy Improvement Actor Critic Framework Critic Regularization

April 25, 2023

What can online reinforcement learning with function approximation benefit from general coverage conditions?
Fanghui Liu, Luca Viano, Volkan Cevher
Reinforcement Learning Online Reinforcement Learning Efficient Reinforcement Learning Function Approximation Sample Efficient Higher Coverage Rate Linear MDPs

March 28, 2023

Function Approximation with Randomly Initialized Neural Networks for Approximate Model Reference Adaptive Control
Tyler Lekang, Andrew Lamperski
Neural Network Activation Function Function Approximation Random Participation Neural Network Approximation Model Reference Adaptive Integral Regression

March 8, 2023

A comparison of rational and neural network based approximations
Vinesha Peiris, Reinier Diaz Millan, Nadezda Sukhorukova, Julien Ugon
Neural Network High Dimensional Consistent Comparison Average Approximation Function Approximation Approximation Algorithm Multivariate Function

February 20, 2023

Reinforcement Learning with Function Approximation: From Linear to Nonlinear
Jihao Long, Jiequn Han
Reinforcement Learning Nonlinear Model Function Approximation Linear Ordered Data Modern Reinforcement Learning Nonlinear Function Approximation

February 13, 2023

Breaking the Curse of Multiagency: Provably Efficient Decentralized Multi-Agent RL with Function Approximation
Yuanhao Wang, Qinghua Liu, Yu Bai, Chi Jin
Multi Agent Reinforcement Learning Markov Game Function Approximation Reversal Curse Tabular Markov Decision Process Decentralized Stochastic Gradient Descent Linear Quadratic

January 23, 2023

On The Convergence Of Policy Iteration-Based Reinforcement Learning With Monte Carlo Policy Evaluation
Anna Winnicki, R. Srikant
Reinforcement Learning Early Stage Convergence Optimal Policy Function Approximation Policy Iteration Health Policy Recommendation Greedy Policy

December 29, 2022

Function Approximation for Solving Stackelberg Equilibrium in Large Perfect Information Games
Chun Kai Ling, J. Zico Kolter, Fei Fang
Function Approximation Zero Sum Game Extensive Form Game General Sum Game Stackelberg Equilibrium Perfect Information Game

November 23, 2022

On Instance-Dependent Bounds for Offline Reinforcement Learning with Linear Function Approximation
Thanh Nguyen-Tang, Ming Yin, Sunil Gupta, Svetha Venkatesh, Raman Arora
Offline Reinforcement Learning Information Theoretic Linear Function Approximation Function Approximation Instance Dependent

October 27, 2022

Beyond the Return: Off-policy Function Estimation under User-specified Error-measuring Distributions
Audrey Huang, Nan Jiang
Regularization Model Policy Evaluation Value Function Customer Service Function Approximation Policy Estimation User Generated Text

September 30, 2022

A General Framework for Sample-Efficient Function Approximation in Reinforcement Learning
Zixiang Chen, Chris Junchi Li, Angela Yuan, Quanquan Gu, Michael I. Jordan
Reinforcement Learning Markov Decision Process General Framework Model Free Reinforcement Learning Function Approximation

September 27, 2022

Continuous approximation by convolutional neural networks with a sigmoidal function
Weike Chang
Neural Network Convolutional Neural Network Function Approximation Sigmoid Function Approximation Capability

September 24, 2022

One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernels
Matthieu Darcy, Boumediene Hamzi, Giulia Livieri, Houman Owhadi, Peyman Tavallali
LeArning Abstract Stochastic Way Stochastic Differential Equation Function Approximation Interacting System Covariance Function Adaptive Kernel

August 25, 2022

CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning
Ben Adcock, Juan M. Cardenas, Nick Dexter
Deep Learning Function Approximation Adaptive Sampling Dimensional Approximation Multivariate Function

June 19, 2022

Guarantees for Epsilon-Greedy Reinforcement Learning with Function Approximation
Christoph Dann, Yishay Mansour, Mehryar Mohri, Ayush Sekhari, Karthik Sridharan
Reinforcement Learning Function Approximation Episodic Markov Decision Process Formal Guarantee Epsilon Greedy Myopic Exploration

June 13, 2022

Analysis of function approximation and stability of general DNNs in directed acyclic graphs using un-rectifying analysis
Wen-Liang Hwang, Shih-Shuo Tung
Neural Network Deep Neural Network General Analysis Function Approximation DNN Architecture Noise Rectification

June 9, 2022

Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint
Hao Liu, Minshuo Chen, Siawpeng Er, Wenjing Liao, Tong Zhang, Tuo Zhao
Native Robustness Generative Adversarial Complementary Benefit Function Approximation Approximation Theory Residual Convolutional Neural Network Smoothness Constraint

Function Approximation

Papers

A Constructive Approach to Function Realization by Neural Stochastic Differential Equations

Effective Minkowski Dimension of Deep Nonparametric Regression: Function Approximation and Statistical Theories

Tackling Heavy-Tailed Rewards in Reinforcement Learning with Function Approximation: Minimax Optimal and Instance-Dependent Regret Bounds

Decision-Aware Actor-Critic with Function Approximation and Theoretical Guarantees

What can online reinforcement learning with function approximation benefit from general coverage conditions?

Function Approximation with Randomly Initialized Neural Networks for Approximate Model Reference Adaptive Control

A comparison of rational and neural network based approximations

Reinforcement Learning with Function Approximation: From Linear to Nonlinear

Breaking the Curse of Multiagency: Provably Efficient Decentralized Multi-Agent RL with Function Approximation

On The Convergence Of Policy Iteration-Based Reinforcement Learning With Monte Carlo Policy Evaluation

Function Approximation for Solving Stackelberg Equilibrium in Large Perfect Information Games

On Instance-Dependent Bounds for Offline Reinforcement Learning with Linear Function Approximation

Beyond the Return: Off-policy Function Estimation under User-specified Error-measuring Distributions

A General Framework for Sample-Efficient Function Approximation in Reinforcement Learning

Continuous approximation by convolutional neural networks with a sigmoidal function

One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernels

CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning

Guarantees for Epsilon-Greedy Reinforcement Learning with Function Approximation

Analysis of function approximation and stability of general DNNs in directed acyclic graphs using un-rectifying analysis

Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint