# Safe and Robust Neural Policy Learning with Statistical Verification for Sim-to-Real Deployment in Robotics

arXiv: https://arxiv.org/abs/2608.06481 · HTML: https://mlsanity.com/paper/2608.06481/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Builds on (most cited first, 29 of 29)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Residual Reinforcement Learning for Robot Control](https://mlsanity.com/paper/1812.03201/) (2018)
- [Robust Deep Reinforcement Learning against Adversarial Perturbations on State Observations](https://mlsanity.com/paper/2003.08938/) (2020)
- [Active Domain Randomization](https://mlsanity.com/paper/1904.04762/) (2019)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [Learning to Walk in the Real World with Minimal Human Effort](https://mlsanity.com/paper/2002.08550/) (2020)
- [Control of a Quadrotor with Reinforcement Learning](https://mlsanity.com/paper/1707.05110/) (2017)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [A Survey of Algorithms for Black-Box Safety Validation of Cyber-Physical Systems](https://mlsanity.com/paper/2005.02979/) (2020)
- [Empirical Design in Reinforcement Learning](https://mlsanity.com/paper/2304.01315/) (2023)
- [safe-control-gym: a Unified Benchmark Suite for Safe Learning-based Control and Reinforcement Learning in Robotics](https://mlsanity.com/paper/2109.06325/) (2021)
- [Efficient Adversarial Training without Attacking: Worst-Case-Aware Robust Reinforcement Learning](https://mlsanity.com/paper/2210.05927/) (2022)
- [Control Regularization for Reduced Variance Reinforcement Learning](https://mlsanity.com/paper/1905.05380/) (2019)
- [Compositional Falsification of Cyber-Physical Systems with Machine Learning Components](https://mlsanity.com/paper/1703.00978/) (2017)
- [Deep Reinforcement Learning Versus Evolution Strategies: A Comparative Survey](https://mlsanity.com/paper/2110.01411/) (2021)
- [Lyapunov Design for Robust and Efficient Robotic Reinforcement Learning](https://mlsanity.com/paper/2208.06721/) (2022)
- [Self-Paced Context Evaluation for Contextual Reinforcement Learning](https://mlsanity.com/paper/2106.05110/) (2021)
- [Physics-Regulated Deep Reinforcement Learning: Invariant Embeddings](https://mlsanity.com/paper/2305.16614/) (2023)
- [Data-driven computation of invariant sets of discrete time-invariant black-box systems](https://mlsanity.com/paper/1907.12075/) (2019)
- [SMC-ES: Automated synthesis of formally verified control policies](https://mlsanity.com/paper/2607.15003/) (2026)
- [Acquire Driving Scenarios Efficiently: A Framework for Prospective Assessment of Cost-Optimal Scenario Acquisition](https://mlsanity.com/paper/2307.11647/) (2023)
- [Beyond Pixels: Learning Invariant Rewards for Real-World Robotics From a Few Demonstrations](https://mlsanity.com/paper/2605.22123/) (2026)

## Built on by (most cited first, 1 of 1)

- [Micro Neural Policies for Safe Real-Time Robotic Control](https://mlsanity.com/paper/2610.08541/) (2026)

## Abstract (arXiv)

Synthesizing safe and robust neural controllers in simulation for reliable sim-to-real deployment remains a critical challenge in robotics. Existing learning-based methods typically lack safety and performance guarantees over an explicitly defined operating region, while post-training verification techniques provide no mechanism to refine controllers when safety violations are detected. To bridge this gap, we propose a curriculum-driven framework that tightly integrates scenario-based Evolution Strategy with Statistical Model Checking-based verification in a closed-loop procedure. Starting from a candidate region, our approach co-optimizes policy performance while progressively enlarging its safe operating boundaries. Upon termination, it yields a neural controller together with a region over which safety and performance are statistically verified. Extensive evaluations on Cartpole and 3D Quadrotor benchmarks, showing 6.14x and 224.04x expansions, respectively, of the safe operating region over mathematically certified ones, together with physical experiments under both nominal conditions and severe dynamic perturbations, demonstrate that our learned controllers consistently outperform established control-theoretic and learning-based baselines. Furthermore, we show that the size of the verified region serves as a quantitative indicator of policy quality before deployment. These results establish our framework as an automated pipeline for learning, assessing and deploying safe and robust neural controllers from simulation to reality.