# Featurized Occupation Measures for Structured Global Search in Numerical Optimal Control

arXiv: https://arxiv.org/abs/2603.16231 · HTML: https://mlsanity.com/paper/2603.16231/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [When Can Depth Replace Precision? A Resource Theory of Quantized Neural Computation](https://mlsanity.com/paper/2607.23390/) (2026)

## Abstract (arXiv)

Numerical optimal control is split between globally structured but dimensionally intractable Hamilton--Jacobi--Bellman (HJB) methods and scalable but local trajectory optimization. We introduce Featurized Occupation Measures (FOM), a finite-dimensional primal--dual interface where HJB subsolutions guide primal search and primal occupation data can inform certificate refinement. Explicit and implicit realizations, based on finite Liouville tests and rollout-sampled residuals, are proved asymptotically consistent with the exact occupation-measure LP. FOM also identifies when HJB-type certificates avoid full state-space representation. For factor graphs induced by compatible passivity-based interconnections, blockwise HJB inequalities yield block-additive OM-dual certificates, including blockwise approximate variants. The curse of dimensionality is then shifted from state dimension to interconnection topology. Approximate certificates remain reusable under time shifts and bounded model perturbations, with explicit degradation bounds. A static obstacle-avoidance benchmark illustrates how tighter certificates improve sample-based global search.