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

March 14, 2024

Minimax Optimal and Computationally Efficient Algorithms for Distributionally Robust Offline Reinforcement Learning
Zhishuai Liu, Pan Xu
Robust Policy Function Approximation Efficient Algorithm Minimax Optimality Robust Offline Reinforcement Learning

February 20, 2024

Learning on manifolds without manifold learning
H. N. Mhaskar, Ryan O'Dowd
LeArning Abstract Average Approximation Manifold Learning Class Manifold Function Approximation Manifold Hypothesis ONE Shot Unknown Manifold

February 17, 2024

Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications
Gianluca Fabiani
Neural Network Average Approximation Function Approximation Practical Application Random Projection Differentiable Activation Function Convergence Theory

February 2, 2024

Two-Timescale Critic-Actor for Average Reward MDPs with Function Approximation
Prashansa Panda, Shalabh Bhatnagar
Actor Critic Algorithm Function Approximation Average Reward MDPs Timescale Actor Critic

January 10, 2024

Experiment Planning with Function Approximation
Aldo Pacchiano, Jonathan N. Lee, Emma Brunskill
Experimental Design Adaptive Learning Function Approximation Contextual Bandit Problem Complex Reward Function

December 16, 2023

A Concentration Bound for TD(0) with Function Approximation
Siddharth Chandak, Vivek S. Borkar
Markov Chain Stochastic Approximation Linear Function Approximation Function Approximation Concentration Bound Concentration Inequality

December 8, 2023

November 28, 2023

Computational Hypergraph Discovery, a Gaussian Process framework for connecting the dots
Théo Bourdais, Pau Batlle, Xianjin Yang, Ricardo Baptista, Nicolas Rouquette, Houman Owhadi
Gaussian Process Function Approximation Dot Product Equation Discovery Hypergraph Structure

November 21, 2023

In-Context Learning Functions with Varying Number of Minima
David Oniani, Yanshan Wang
Context Learning Numerical Data Two Layer Neural Network Function Approximation

November 7, 2023

Structure of universal formulas
Dmitry Yarotsky
Inner Structure Universal Approximation Function Approximation Functional Map Universal Formula Polynomial Complexity

October 30, 2023

October 11, 2023

Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuits
Zhan Yu, Qiuhao Chen, Yuling Jiao, Yinan Li, Xiliang Lu, Xin Wang, Jerry Zhijian Yang
Quantum Machine Learning Universal Approximation Function Approximation Parameterized Quantum Circuit Provable Benefit Quantum Signal

August 13, 2023

Separable Gaussian Neural Networks: Structure, Analysis, and Function Approximations
Siyuan Xing, Jianqiao Sun
Neural Network General Analysis Inner Structure Function Approximation Radial Basis Function Gaussian Data Separable Gaussian Neural Network

July 25, 2023

The Optimal Approximation Factors in Misspecified Off-Policy Value Function Estimation
Philip Amortila, Nan Jiang, Csaba Szepesvári
Reinforcement Learning Function Approximation Policy Estimation Constant Factor Approximation

July 24, 2023

July 17, 2023

Natural Actor-Critic for Robust Reinforcement Learning with Function Approximation
Ruida Zhou, Tao Liu, Min Cheng, Dileep Kalathil, P. R. Kumar, Chao Tian
Robust Reinforcement Learning Function Approximation Optimal Robust Policy Robust Policy Evaluation

July 6, 2023

Provably Efficient Iterated CVaR Reinforcement Learning with Function Approximation and Human Feedback
Yu Chen, Yihan Du, Pihe Hu, Siwei Wang, Desheng Wu, Longbo Huang
Human Feedback Function Approximation Risk Sensitive Reinforcement Learning Value at Risk

Function Approximation

Papers

Minimax Optimal and Computationally Efficient Algorithms for Distributionally Robust Offline Reinforcement Learning

Learning on manifolds without manifold learning

Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications

Two-Timescale Critic-Actor for Average Reward MDPs with Function Approximation

Experiment Planning with Function Approximation

A Concentration Bound for TD(0) with Function Approximation

On the Performance of Temporal Difference Learning With Neural Networks

Two-Timescale Q-Learning with Function Approximation in Zero-Sum Stochastic Games

Computational Hypergraph Discovery, a Gaussian Process framework for connecting the dots

In-Context Learning Functions with Varying Number of Minima

Structure of universal formulas

Posterior Sampling for Competitive RL: Function Approximation and Partial Observation

Approximation Theory, Computing, and Deep Learning on the Wasserstein Space

Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuits

Separable Gaussian Neural Networks: Structure, Analysis, and Function Approximations

The Optimal Approximation Factors in Misspecified Off-Policy Value Function Estimation

Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirs

Rates of Approximation by ReLU Shallow Neural Networks

Natural Actor-Critic for Robust Reinforcement Learning with Function Approximation

Provably Efficient Iterated CVaR Reinforcement Learning with Function Approximation and Human Feedback