# Error Propagation in Dynamic Programming: From Stochastic Control to American Option Pricing

arXiv: https://arxiv.org/abs/2509.20239 · HTML: https://mlsanity.com/paper/2509.20239/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 64 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [An optimal control perspective on diffusion-based generative modeling](https://mlsanity.com/paper/2211.01364/) (2022)
- [Improved sampling via learned diffusions](https://mlsanity.com/paper/2307.01198/) (2023)
- [Kernel methods through the roof: handling billions of points efficiently](https://mlsanity.com/paper/2006.10350/) (2020)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Stochastic Optimal Control Matching](https://mlsanity.com/paper/2312.02027/) (2023)
- [Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Paths](https://mlsanity.com/paper/2207.02149/) (2022)
- [Deep Relaxation: partial differential equations for optimizing deep neural networks](https://mlsanity.com/paper/1704.04932/) (2017)
- [High-Dimensional Stochastic Optimal Control using Continuous Tensor Decompositions](https://mlsanity.com/paper/1611.04706/) (2016)
- [The Nystr"om method for convex loss functions](https://mlsanity.com/paper/2006.10016/) (2020)
- [Computational Efficiency under Covariate Shift in Kernel Ridge Regression](https://mlsanity.com/paper/2505.14083/) (2025)

## Abstract (arXiv)

This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing the mathematical structure needed for a detailed convergence analysis. The associate value function is estimated through a sequence of approximations combining nonparametric regression methods and Monte Carlo subsampling. The regression step is performed within reproducing kernel Hilbert spaces (RKHSs), exploiting the classical KRR algorithm, while Monte Carlo sampling methods are introduced to estimate the continuation value. To assess the accuracy of our value function estimator, we propose a natural error decomposition and rigorously control the resulting error terms at each time step. We then analyze how this error propagates backward in time-from maturity to the initial stage-a relatively underexplored aspect of the SOC literature. Finally, we illustrate how our analysis naturally applies to a key financial application: the pricing of American options.