Search Results for author: Jihao Long

Found 11 papers, 1 papers with code

A Duality Analysis of Kernel Ridge Regression in the Noiseless Regime

no code implementations24 Feb 2024 Jihao Long, Xiaojun Peng, Lei Wu

In this paper, we conduct a comprehensive analysis of generalization properties of Kernel Ridge Regression (KRR) in the noiseless regime, a scenario crucial to scientific computing, where data are often generated via computer simulations.

regression

The $L^\infty$ Learnability of Reproducing Kernel Hilbert Spaces

no code implementations5 Jun 2023 Hongrui Chen, Jihao Long, Lei Wu

We prove that if $\beta$ is independent of the input dimension $d$, then functions in the RKHS can be learned efficiently under the $L^\infty$ norm, i. e., the sample complexity depends polynomially on $d$.

A duality framework for generalization analysis of random feature models and two-layer neural networks

no code implementations9 May 2023 Hongrui Chen, Jihao Long, Lei Wu

The first application is to study learning functions in $\mathcal{F}_{p,\pi}$ with RFMs.

Reinforcement Learning with Function Approximation: From Linear to Nonlinear

no code implementations20 Feb 2023 Jihao Long, Jiequn Han

These results rely on the $L^\infty$ and UCB estimation of estimation error, which can handle the distribution mismatch phenomenon.

reinforcement-learning Reinforcement Learning (RL)

Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence

1 code implementation25 Apr 2022 Jiequn Han, Ruimeng Hu, Jihao Long

These coefficient functions are used to approximate the MV-FBSDEs' model coefficients with full distribution dependence, and are updated by solving another supervising learning problem using training data simulated from the last iteration's FBSDE solutions.

Perturbational Complexity by Distribution Mismatch: A Systematic Analysis of Reinforcement Learning in Reproducing Kernel Hilbert Space

no code implementations5 Nov 2021 Jihao Long, Jiequn Han

As a byproduct, we show that when the reward functions lie in a high dimensional RKHS, even if the transition probability is known and the action space is finite, it is still possible for RL problems to suffer from the curse of dimensionality.

Reinforcement Learning (RL)

A spectral-based analysis of the separation between two-layer neural networks and linear methods

no code implementations10 Aug 2021 Lei Wu, Jihao Long

We propose a spectral-based approach to analyze how two-layer neural networks separate from linear methods in terms of approximating high-dimensional functions.

A Class of Dimension-free Metrics for the Convergence of Empirical Measures

no code implementations24 Apr 2021 Jiequn Han, Ruimeng Hu, Jihao Long

The proposed metrics fall into the category of integral probability metrics, for which we specify criteria of test function spaces to guarantee the property of being free of CoD.

An $L^2$ Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation

no code implementations15 Apr 2021 Jihao Long, Jiequn Han, Weinan E

Reinforcement learning (RL) algorithms based on high-dimensional function approximation have achieved tremendous empirical success in large-scale problems with an enormous number of states.

Reinforcement Learning (RL)

Convergence of Deep Fictitious Play for Stochastic Differential Games

no code implementations12 Aug 2020 Jiequn Han, Ruimeng Hu, Jihao Long

Stochastic differential games have been used extensively to model agents' competitions in Finance, for instance, in P2P lending platforms from the Fintech industry, the banking system for systemic risk, and insurance markets.

BIG-bench Machine Learning

Convergence of the Deep BSDE Method for Coupled FBSDEs

no code implementations3 Nov 2018 Jiequn Han, Jihao Long

The recently proposed numerical algorithm, deep BSDE method, has shown remarkable performance in solving high-dimensional forward-backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs).

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