# Promises of Deep Kernel Learning for Control Synthesis

arXiv: https://arxiv.org/abs/2309.06569 · HTML: https://mlsanity.com/paper/2309.06569/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 12 Sep 2023.

## Builds on (most cited first, 14 of 14)

- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [The Promises and Pitfalls of Deep Kernel Learning](https://mlsanity.com/paper/2102.12108/) (2021)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [Planning with Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constants](https://mlsanity.com/paper/2010.08993/) (2020)
- [Safe Control with Neural Network Dynamic Models](https://mlsanity.com/paper/2110.01110/) (2021)
- [Safety Guarantees for Neural Network Dynamic Systems via Stochastic Barrier Functions](https://mlsanity.com/paper/2206.07811/) (2022)
- [Efficiency through Uncertainty: Scalable Formal Synthesis for Stochastic Hybrid Systems](https://mlsanity.com/paper/1901.01576/) (2019)
- [Formal Control Synthesis for Stochastic Neural Network Dynamic Models](https://mlsanity.com/paper/2203.05903/) (2022)
- [Strategy Synthesis for Partially-known Switched Stochastic Systems](https://mlsanity.com/paper/2104.02172/) (2021)
- [Adversarial Robustness Guarantees for Gaussian Processes](https://mlsanity.com/paper/2104.03180/) (2021)
- [Formal Verification of Unknown Dynamical Systems via Gaussian Process Regression](https://mlsanity.com/paper/2201.00655/) (2021)
- [Interval Markov Decision Processes with Continuous Action-Spaces](https://mlsanity.com/paper/2211.01231/) (2022)
- [Data-driven and Model-based Verification: a Bayesian Identification Approach](https://mlsanity.com/paper/1509.03347/) (2015)

## Built on by (most cited first, 4 of 4)

- [Error Bounds For Gaussian Process Regression Under Bounded Support Noise With Applications To Safety Certification](https://mlsanity.com/paper/2408.09033/) (2024)
- [Learning-Based Shielding for Safe Autonomy under Unknown Dynamics](https://mlsanity.com/paper/2410.07359/) (2024)
- [Verification of Unknown Dynamical Systems via Autoencoder Latent Space](https://mlsanity.com/paper/2512.13593/) (2025)
- [ActivePusher: Active Learning and Planning with Residual Physics for Nonprehensile Manipulation](https://mlsanity.com/paper/2506.04646/) (2025)

## Abstract (arXiv)

Deep Kernel Learning (DKL) combines the representational power of neural networks with the uncertainty quantification of Gaussian Processes. Hence, it is potentially a promising tool to learn and control complex dynamical systems. In this work, we develop a scalable abstraction-based framework that enables the use of DKL for control synthesis of stochastic dynamical systems against complex specifications. Specifically, we consider temporal logic specifications and create an end-to-end framework that uses DKL to learn an unknown system from data and formally abstracts the DKL model into an Interval Markov Decision Process (IMDP) to perform control synthesis with correctness guarantees. Furthermore, we identify a deep architecture that enables accurate learning and efficient abstraction computation. The effectiveness of our approach is illustrated on various benchmarks, including a 5-D nonlinear stochastic system, showing how control synthesis with DKL can substantially outperform state-of-the-art competitive methods.