no code implementations • 24 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.
no code implementations • 5 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 $d$.
no code implementations • 9 May 2023 • Hongrui Chen, Jihao Long, Lei Wu
The first application is to study learning functions in $\mathcal{F}_{p,\pi}$ with RFMs.
no code implementations • 20 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.
1 code implementation • 25 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.
no code implementations • 5 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.
no code implementations • 10 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.
no code implementations • 24 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.
no code implementations • 15 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.
no code implementations • 12 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.
no code implementations • 3 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).