Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations — Paper

Abstract

We analyze a neural semi-discrete method for high-dimensional first-order Hamilton-Jacobi-Bellman (HJB) equations with known or learned dynamics. Centered differences and an artificial viscosity $Nh=O(h)$ define a monotone operator evaluated through $2d+1$ shifted network queries; policy iteration solves the resulting Bellman equation without a tensor grid. At fixed $h$, the sharp componentwise condition $\max_i|f_i|\le2N$ turns every frozen-policy operator into a nearest-neighbor Markov-chain generator with a policy-independent total jump rate. Uniformization gives whole-space well-posedness for measurable feedbacks, an explicit Poisson-tail bound on the numerical domain of dependence, and boundary-free localization. The representation also yields a posteriori policy-evaluation bounds that account for residual and learned-model errors. A greedy-gap analysis controls inexact policy iteration at fixed $h$; a separate consistency estimate connects the semi-discrete equation to the continuous HJB equation. Experiments reproduce the extremal tail, show rates consistent with $O(\sqrt h)$ and nearly $h$-independent exact-policy-iteration decay, and assess empirical estimator effectivity. A nonsmooth example shows that the continuous residual can miss a non-viscosity solution, whereas the shifted residual detects the defect. Further tests provide a structured interval-verified certificate calibration, an early-budget benefit of policy freezing for bang-bang control, and learned-dynamics diagnostics. A structured nonlinear problem with active compact-control constraints is tested against a manufactured semi-discrete reference through $d=1024$.

Authors 4

Minseok Kim, Yeongjong Kim, Namkyeong Cho, Yeoneung Kim

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Official page: arxiv.org/abs/2605.07116
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Arxiv announce type: replace
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
arXiv id: 2605.07116
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Categories: cs.LG, cs.AI, cs.NA, math.NA, math.OC
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
PDF: arxiv.org/pdf/2605.07116
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Primary category: cs.LG
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh

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9

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T19

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2 h ago

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Authors: Minseok Kim, Yeongjong Kim, Namkyeong Cho

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Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/pdf/2605.07116	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperMonotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations
New paper: Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations
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Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	10 min ago	1

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