# Infinite-dimensional spherical-radial decomposition for probabilistic functions, with application to constrained optimal control and Gaussian process regression

arXiv: https://arxiv.org/abs/2603.19907 · HTML: https://mlsanity.com/paper/2603.19907/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 22 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 6 of 6)

- [A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges](https://mlsanity.com/paper/2006.09319/) (2020)
- [Nonnegativity-Enforced Gaussian Process Regression](https://mlsanity.com/paper/2004.04632/) (2020)
- [Solving Chance-Constrained Problems via a Smooth Sample-Based Nonlinear Approximation](https://mlsanity.com/paper/1905.07377/) (2019)
- [Optimality conditions in control problems with random state constraints in probabilistic or almost-sure form](https://mlsanity.com/paper/2306.03965/) (2023)
- [Numerical solution of an optimal control problem with probabilistic and almost sure state constraints](https://mlsanity.com/paper/2311.15115/) (2023)
- [Optimal control under uncertainty with joint chance state constraints: almost-everywhere bounds, variance reduction, and application to (bi-)linear elliptic PDEs](https://mlsanity.com/paper/2412.05125/) (2024)

## Abstract (arXiv)

The spherical-radial decomposition (SRD) is an efficient method for estimating probabilistic functions and their gradients defined over finite-dimensional elliptical distributions. In this work, we generalize the SRD to infinite stochastic dimensions by combining subspace SRD with standard Monte Carlo methods. The resulting method, which we call hybrid infinite-dimensional SRD (hiSRD) provides an unbiased, low-variance estimator for convex sets arising, for instance, in chance-constrained optimization. We provide a theoretical analysis of the variance of finite-dimensional SRD as the dimension increases, and show that the proposed hybrid method eliminates truncation-induced bias, reduces variance, and allows the computation of derivatives of probabilistic functions. We present comprehensive numerical studies for a risk-neutral stochastic PDE optimal control problem with joint chance state constraints, and for optimizing kernel parameters in Gaussian process regression under the constraint that the posterior process satisfies joint chance constraints.