# Safe Guaranteed Exploration for Non-linear Systems

arXiv: https://arxiv.org/abs/2402.06562 · HTML: https://mlsanity.com/paper/2402.06562/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 45 references that are in the map.
- First posted on arXiv 9 Feb 2024.

## Builds on (most cited first, 21 of 21)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [A predictive safety filter for learning-based control of constrained nonlinear dynamical systems](https://mlsanity.com/paper/1812.05506/) (2018)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [Safe Exploration in Finite Markov Decision Processes with Gaussian Processes](https://mlsanity.com/paper/1606.04753/) (2016)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [Safe Exploration for Interactive Machine Learning](https://mlsanity.com/paper/1910.13726/) (2019)
- [Submodular Reinforcement Learning](https://mlsanity.com/paper/2307.13372/) (2023)
- [FASTER: Fast and Safe Trajectory Planner for Navigation in Unknown Environments](https://mlsanity.com/paper/2001.04420/) (2020)
- [Near-Optimal Multi-Agent Learning for Safe Coverage Control](https://mlsanity.com/paper/2210.06380/) (2022)
- [Autonomous Teamed Exploration of Subterranean Environments using Legged and Aerial Robots](https://mlsanity.com/paper/2111.06482/) (2021)
- [Zero-Order Optimization for Gaussian Process-based Model Predictive Control](https://mlsanity.com/paper/2211.15522/) (2022)
- [Analysis and design of model predictive control frameworks for dynamic operation -- An overview](https://mlsanity.com/paper/2307.03004/) (2023)
- [Safe Trajectory Tracking in Uncertain Environments](https://mlsanity.com/paper/2001.11602/) (2020)
- [Safe Exploration and Escape Local Minima with Model Predictive Control under Partially Unknown Constraints](https://mlsanity.com/paper/2205.03614/) (2022)

## Built on by (most cited first, 8 of 8)

- [Performance-driven Constrained Optimal Auto-Tuner for MPC](https://mlsanity.com/paper/2503.07127/) (2025)
- [Safe Exploration via Policy Priors](https://mlsanity.com/paper/2601.19612/) (2026)
- [Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics](https://mlsanity.com/paper/2505.07594/) (2025)
- [Safe and Near-Optimal Control with Online Dynamics Learning](https://mlsanity.com/paper/2509.16650/) (2025)
- [Safely Learning Controlled Stochastic Dynamics](https://mlsanity.com/paper/2506.02754/) (2025)
- [A robust and adaptive MPC formulation for Gaussian process models](https://mlsanity.com/paper/2507.02098/) (2025)
- [Sampling-Based Safe Reinforcement Learning](https://mlsanity.com/paper/2605.19469/) (2026)
- [Directional Constraints for Efficient Exploration in Safe Reinforcement Learning](https://mlsanity.com/paper/2607.12784/) (2026)

## Abstract (arXiv)

Safely exploring environments with a-priori unknown constraints is a fundamental challenge that restricts the autonomy of robots. While safety is paramount, guarantees on sufficient exploration are also crucial for ensuring autonomous task completion. To address these challenges, we propose a novel safe guaranteed exploration framework using optimal control, which achieves first-of-its-kind results: guaranteed exploration for non-linear systems with finite time sample complexity bounds, while being provably safe with arbitrarily high probability. The framework is general and applicable to many real-world scenarios with complex non-linear dynamics and unknown domains. We improve the efficiency of this general framework by proposing an algorithm, SageMPC, SAfe Guaranteed Exploration using Model Predictive Control. SageMPC leverages three key techniques: i) exploiting a Lipschitz bound, ii) goal-directed exploration, and iii) receding horizon style re-planning, all while maintaining the desired sample complexity, safety and exploration guarantees of the framework. Lastly, we demonstrate safe efficient exploration in challenging unknown environments using SageMPC with a car model.