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New method solves high-dimensional HJB equations using neural networks

By PulseAugur Editorial · [1 sources] ·

Researchers have developed a novel physics-informed policy iteration method designed to solve high-dimensional Hamilton--Jacobi--Bellman equations, which are crucial in continuous-time stochastic control. This method utilizes a mesh-free neural residual solver for each policy-evaluation step, approximating elliptic PDEs, and then performs policy improvement pointwise using the surrogate gradient. The analysis demonstrates well-posedness for Borel Markov policies and establishes Lipschitz stability for the greedy map, providing a finite-step interior error bound that is influenced by a continuous L^p residual and an attenuated boundary term. Experiments on various test cases, including a 100-dimensional problem, show the method's effectiveness, though limitations related to collocation distribution and gradient determination without boundary data were also identified. AI

IMPACT This research could advance AI capabilities in complex control systems and optimization problems.

RANK_REASON The cluster contains a research paper detailing a new method for solving complex mathematical equations relevant to AI and control theory. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

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New method solves high-dimensional HJB equations using neural networks

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The cluster contains a research paper detailing a new method for solving complex mathematical equations relevant to AI and control theory. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Yeongjong Kim, Minseok Kim, Yeoneung Kim, Namkyeong Cho ·

    Physics-Informed Policy Iteration for High-Dimensional Hamilton--Jacobi--Bellman Equations: Interior Error Bounds without Boundary Data

    arXiv:2508.01718v2 Announce Type: replace Abstract: We develop a physics-informed policy-iteration method for stationary second-order Hamilton--Jacobi--Bellman equations arising in continuous-time stochastic control. Each policy-evaluation step is a linear elliptic PDE and is app…

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