# Distributionally Robust Optimal and Safe Control of Stochastic Systems via Kernel Conditional Mean Embedding

arXiv: https://arxiv.org/abs/2304.00644 · HTML: https://mlsanity.com/paper/2304.00644/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2023.

## Built on by (most cited first, 6 of 6)

- [Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddings](https://mlsanity.com/paper/2403.10497/) (2024)
- [Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets](https://mlsanity.com/paper/2505.03585/) (2025)
- [Distributionally Robust Control with End-to-End Statistically Guaranteed Metric Learning](https://mlsanity.com/paper/2510.10214/) (2025)
- [Kernel-Based Learning of Safety Barriers](https://mlsanity.com/paper/2601.12002/) (2026)
- [Safety Certification is Classification](https://mlsanity.com/paper/2605.06087/) (2026)
- [Kernel-Based Safe Exploration in Deep Reinforcement Learning](https://mlsanity.com/paper/2605.22207/) (2026)

## Abstract (arXiv)

We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the state evolution into an associated repreducing kernel Hilbert space. Our key idea lies in combining conditional mean embedding with the maximum mean discrepancy distance to construct an ambiguity set, and then design a robust control policy using techniques from distributionally robust optimization. The main theoretical contribution of this paper is to leverage functional analytic tools to prove that optimal policies for this infinite-dimensional min-max problem are Markovian and deterministic. Additionally, we discuss approximation schemes based on state and input discretization to make the approach computationally tractable. To validate the theoretical findings, we conduct an experiment on safe control for thermostatically controlled loads (TCL).