139 citations · 170 across the 18 of their papers we have counts for
18 papers
Optimal Weighted Hessian Estimates for Parabolic Equations under General Diffusion Marginals
Jihao Long, Zhenhua Zhao
We study weighted Hessian estimates for parabolic terminal equations under the marginals of a prescribed diffusion, allowing singular initial laws and different principal coe…
Deep Stochastic Residual Methods for Fully Nonlinear Parabolic Equations
Zhenhua Zhao, Jihao Long
We develop and analyze neural stochastic residual methods for fully nonlinear parabolic terminal problems under exact diffusion sampling. A quadratic stochastic residual supports g…
Deep Picard Iteration for High-Dimensional Nonlinear PDEs
Jiequn Han, Wei Hu, Jihao Long +1
We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies…
Learning Free Terminal Time Optimal Closed-loop Control of Manipulators
Wei Hu, Yue Zhao, Weinan E +2
This paper presents a novel approach to learning free terminal time closed-loop control for robotic manipulation tasks, enabling dynamic adjustment of task duration and control inp…
The Learnability of Reproducing Kernel Hilbert Spaces
Hongrui Chen, Jihao Long, Lei Wu
In this work, we analyze the learnability of reproducing kernel Hilbert spaces (RKHS) under the norm, which is critical for understanding the performance of kernel metho…
A duality framework for analyzing random feature and two-layer neural networks
Hongrui Chen, Jihao Long, Lei Wu
We consider the problem of learning functions within the and Barron spaces, which play crucial roles in understanding random feature models (RFMs), two-layer ne…
Reinforcement Learning with Function Approximation: From Linear to Nonlinear
Jihao Long, Jiequn Han
Function approximation has been an indispensable component in modern reinforcement learning algorithms designed to tackle problems with large state spaces in high dimensions. This…
Progressive Optimal Path Sampling for Closed-Loop Optimal Control Design with Deep Neural Networks
Xuanxi Zhang, Jihao Long, Wei Hu +2
Closed-loop optimal control design for high-dimensional nonlinear systems has been a long-standing challenge. Traditional methods, such as solving the associated Hamilton-Jacobi-Be…
Solving Optimal Control Problems of Rigid-Body Dynamics with Collisions Using the Hybrid Minimum Principle
Wei Hu, Jihao Long, Yaohua Zang +2
Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states…
Empowering Optimal Control with Machine Learning: A Perspective from Model Predictive Control
Weinan E, Jiequn Han, Jihao Long
Solving complex optimal control problems have confronted computational challenges for a long time. Recent advances in machine learning have provided us with new opportunities to ad…
Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence
Jiequn Han, Ruimeng Hu, Jihao Long
One of the core problems in mean-field control and mean-field games is to solve the corresponding McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). Most…
A Machine Learning Enhanced Algorithm for the Optimal Landing Problem
Yaohua Zang, Jihao Long, Xuanxi Zhang +3
We propose a machine learning enhanced algorithm for solving the optimal landing problem. Using Pontryagin's minimum principle, we derive a two-point boundary value problem for the…
Perturbational Complexity by Distribution Mismatch: A Systematic Analysis of Reinforcement Learning in Reproducing Kernel Hilbert Space
Jihao Long, Jiequn Han
Most existing theoretical analysis of reinforcement learning (RL) is limited to the tabular setting or linear models due to the difficulty in dealing with function approximation in…
A spectral-based analysis of the separation between two-layer neural networks and linear methods
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. We show that quanti…
A Class of Dimension-free Metrics for the Convergence of Empirical Measures
Jiequn Han, Ruimeng Hu, Jihao Long
This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is fre…
An Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation
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 o…
Convergence of Deep Fictitious Play for Stochastic Differential Games
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 sys…
Convergence of the Deep BSDE Method for Coupled FBSDEs
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…