# Robust Regression for Safe Exploration in Control

arXiv: https://arxiv.org/abs/1906.05819 · HTML: https://mlsanity.com/paper/1906.05819/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2019.

## Built on by (most cited first, 24 of 24)

- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021)
- [Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guarantees](https://mlsanity.com/paper/2201.08355/) (2022)
- [Stability Verification in Stochastic Control Systems via Neural Network Supermartingales](https://mlsanity.com/paper/2112.09495/) (2021)
- [Meta-Adaptive Nonlinear Control: Theory and Algorithms](https://mlsanity.com/paper/2106.06098/) (2021)
- [Learning Control Policies for Stochastic Systems with Reach-avoid Guarantees](https://mlsanity.com/paper/2210.05308/) (2022)
- [Escaping from Zero Gradient: Revisiting Action-Constrained Reinforcement Learning via Frank-Wolfe Policy Optimization](https://mlsanity.com/paper/2102.11055/) (2021)
- [Minimax Model Learning](https://mlsanity.com/paper/2103.02084/) (2021)
- [A Human-Centered Safe Robot Reinforcement Learning Framework with Interactive Behaviors](https://mlsanity.com/paper/2302.13137/) (2023)
- [Compositional Policy Learning in Stochastic Control Systems with Formal Guarantees](https://mlsanity.com/paper/2312.01456/) (2023)
- [How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equations](https://mlsanity.com/paper/2306.06335/) (2023)
- [Safe Deep Policy Adaptation](https://mlsanity.com/paper/2310.08602/) (2023)
- [Reactive and Safe Road User Simulations using Neural Barrier Certificates](https://mlsanity.com/paper/2109.06689/) (2021)
- [Provably Correct Training of Neural Network Controllers Using Reachability Analysis](https://mlsanity.com/paper/2102.10806/) (2021)
- [Learning Provably Stabilizing Neural Controllers for Discrete-Time Stochastic Systems](https://mlsanity.com/paper/2210.05304/) (2022)
- [Distributionally Robust Policy Evaluation under General Covariate Shift in Contextual Bandits](https://mlsanity.com/paper/2401.11353/) (2024)
- [ConBaT: Control Barrier Transformer for Safe Policy Learning](https://mlsanity.com/paper/2303.04212/) (2023)
- [Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertainty](https://mlsanity.com/paper/2501.04757/) (2025)
- [Action-Constrained Imitation Learning](https://mlsanity.com/paper/2508.14379/) (2025)
- [Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learning](https://mlsanity.com/paper/2307.00828/) (2023)
- [Automatic Optimisation of Normalised Neural Networks](https://mlsanity.com/paper/2312.10672/) (2023)
- [Learning to Control an Unstable System with One Minute of Data: Leveraging Gaussian Process Differentiation in Predictive Control](https://mlsanity.com/paper/2103.04548/) (2021)
- [Probabilistic Counterexample Guidance for Safer Reinforcement Learning (Extended Version)](https://mlsanity.com/paper/2307.04927/) (2023)
- [Contraction-Aware Reinforcement Learning for Nonlinear Control with Statistical Robustness](https://mlsanity.com/paper/2506.15700/) (2025)

## Abstract (arXiv)

We study the problem of safe learning and exploration in sequential control problems. The goal is to safely collect data samples from operating in an environment, in order to learn to achieve a challenging control goal (e.g., an agile maneuver close to a boundary). A central challenge in this setting is how to quantify uncertainty in order to choose provably-safe actions that allow us to collect informative data and reduce uncertainty, thereby achieving both improved controller safety and optimality. To address this challenge, we present a deep robust regression model that is trained to directly predict the uncertainty bounds for safe exploration. We derive generalization bounds for learning, and connect them with safety and stability bounds in control. We demonstrate empirically that our robust regression approach can outperform the conventional Gaussian process (GP) based safe exploration in settings where it is difficult to specify a good GP prior.