HJB Equations

HJB: Hamilton-Jacobi-Bellman

Latest papers

17 papers0 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Learning to Solve Stochastic Controls with Unknown Drifts and Running Rewards: Theory, Algorithms and Convergence
Sep 14, 2026Jin Ma, Gaozhan Wang, Jianfeng Zhang +1Reinforcement Learning Stochastic Optimal Control
Department of Mathematics, University of Southern California, Los Angeles, CA 90089 · Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027
Tensor Train Diffusion: Leveraging Low-Rank Structures for High-Dimensional Score-Based Sampling
Jul 7, 2026Robert Gruhlke, Julius Berner, David Sommer +1Stochastic Differential Equations Diffusion Sampling
Freie Universität Berlin · NVIDIA · WIAS +2
Mean-Field PhiBE: Continuous-Time Mean-Field Reinforcement Learning from Discrete-Time Data
Jun 25, 2026Erhan Bayraktar, Martin Hernandez, Qinxin Yan +1Actor-Critic Methods Stochastic Optimal Control
Department of Mathematics, University of Michigan, Ann Arbor, MI, USA. · Department of Statistics and Data Science, University of California, Los Angeles, CA, USA. · Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, USA.
Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEs
Jun 22, 2026Matías Gómez-Aedo, Behzad Azmi, Yuyang Huang +2Value Function Estimation PDE Solving
Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ London, UK · Department of Mathematics and Statistics, University of Konstanz, Germany · RICAM and Institute of Mathematics and Scientific Computing, University of Graz, Austria
Computing Smooth Geodesics under Two-Sided Curvature Bounds with Applications to Robotics and Image Analysis
Jun 11, 2026Da Chen, Zhenjiang Li, Jean-Marie Mirebeau +4HJB Equations Motion Planning
CEREMADE, University Paris Dauphine, University-PSL, CNRS, UMR 7534, Paris, 75775, France · Department of Radiation Oncology, Shandong Cancer Hospital and Institute, Shandong First Medical University, Shandong Academy of Medical Sciences, Jinan, 250117, China · Department of Mathematics, Centre Borelli, ENS Paris-Saclay, CNRS, University Paris-Saclay, Gif-sur-Yvette, 91190, France +2
Autopilot-Preserving Residual Q-Learning with HJB-Inspired Finite-Action Risk Filtering for Fixed-Wing UAV Command Supervision
May 31, 2026Mehmet Iscan, Batuhan TemizAerial Robotics Stochastic Optimal Control
PythaLab, Yildiz Technical University, Istanbul, Turkey · Autopilot Systems Chief Engineer, Turkish Aerospace (TUSAŞ), Ankara, Turkey
A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent Lévy Jumps
May 31, 2026R. DrissiNeural PDE Solvers Stochastic Optimal Control
Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations
May 8, 2026Minseok Kim, Yeongjong Kim, Namkyeong Cho +1Neural PDE Solvers Stochastic Optimal Control
Department of Applied Artificial Intelligence, Seoul National University of Science and Technology, Seoul, Republic of Korea. · Department of Mathematics, Pohang University of Science and Technology, Pohang, Republic of Korea. · Department of Mathematical Finance and Big Data, Gachon University, Seongnam, Republic of Korea +1
Generative optimal transport via forward-backward HJB matching
Apr 9, 2026Haiqian Yang, Vishaal Krishnan, Sumit Sinha +1HJB Equations Stochastic Optimal Control
Department of Mechanical Engineering, MIT, Cambridge, MA 02139 · SEAS, Harvard University, Cambridge, MA 02138 · SEAS, Physics and OEB, Harvard University, Cambridge, MA 02138
A Schrödinger Eigenfunction Method for Long-Horizon Stochastic Optimal Control
Mar 24, 2026Louis Claeys, Artur Goldman, Zebang Shen +1Stochastic Optimal Control HJB Equations
ETH Zürich, Department of Mathematics · ETH Zürich, ETH AI Center, Institute for Machine Learning · ETH Zürich, Institute for Machine Learning
Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equations
Mar 20, 2026Jun LiuHJB Equations Neural PDE Solvers
Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control
Mar 19, 2026Samuel N. Cohen, Filippo de Feo, Jackson Hebner +1HJB Equations PDE Solving
Mathematical Institute, University of Oxford · Institut für Mathematik, Technische Universität Berlin
Featurized Occupation Measures for Structured Global Search in Numerical Optimal Control
Mar 17, 2026Qi Wei, Jianfeng Tao, Haoyang Tan +1HJB Equations Optimal Control
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Quantum mechanical framework for quantization-based optimization: from Gradient flow to Schroedinger equation
Mar 12, 2026Jinwuk Seok, Changsik ChoHJB Equations Global Optimization
On-Device AIM Research Section AIC Research Lab, ETRI Daejeon, Rep. Korea
RAmmStein: Regime Adaptation in Mean-reverting Markets with Stein Thresholds -- Optimal Impulse Control in Concentrated AMMs
Feb 23, 2026Pranay AnchuriHJB Equations Decentralized Finance
Offchain Labs
Gaussian process policy iteration with additive Schwarz acceleration for forward and inverse HJB and mean field game problems
May 1, 2025Xianjin Yang, Jingguo ZhangMean Field Games Stochastic Optimal Control
Department of Computing and Mathematical Sciences, California Institute of Technology, CA, USA. · Department of Mathematics and Risk Management Institute, National University of Singapore, Singapore.
Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spaces
Jul 23, 2024Nicolas Hoischen, Petar Bevanda, Stefan Sosnowski +2HJB Equations Stochastic Optimal Control
Chair of Information-oriented Control, TU Munich, Germany · School of Information Science and Technology, ShanghaiTech University, China

Sep 14, 2026J/K move · Enter open · S save

Learning to Solve Stochastic Controls with Unknown Drifts and Running Rewards: Theory, Algorithms and Convergence

Jin Ma, Gaozhan Wang, Jianfeng Zhang, Xunyu Zhou

Department of Mathematics, University of Southern California, Los Angeles, CA 90089 · Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027

Reinforcement Learning Stochastic Optimal Control Policy Iteration RL Exploration Maximum Entropy RL Continuous-Time RL+1

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We study continuous-time and possibly high-dimensional stochastic control problems where drift coefficients and running reward functions are unknown. Due to these missing model primitives, we take the exploratory, reinforcement learning (RL) framework of Wang, Zariphopoulou, and Zhou(2020) with relaxed controls and entropy regularization. The objective is to develop theoretically grounded, efficient and scalable RL algorithms to learn both the optimal value functions (which also solve the exploratory HJB equation) and optimal exploratory feedback control policies. When the diffusion coefficients do not contain control, we employ probabilistic representations of both the optimal value function and its gradient based on an auxiliary state process depending only on the diffusion part of the original dynamics. With a delicate analysis on some properly defined mappings and their fixed points, this leads to the introduction of our policy iteration algorithms and their convergence. We demonstrate the performance of our algorithms through various numerical examples. Finally, we study a special control-dependent diffusion case where probability representation of the Hessian is called for.