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1. Guiding Safe Exploration with Weakest Preconditions

   Greg Anderson; Swarat Chaudhuri; Isil Dillig (January 2023, International Conference on Learning Representations)

   In reinforcement learning for safety-critical settings, it is often desirable for the agent to obey safety constraints at all points in time, including during training. We present a novel neurosymbolic approach called SPICE to solve this safe exploration problem. SPICE uses an online shielding layer based on symbolic weakest preconditions to achieve a more precise safety analysis than existing tools without unduly impacting the training process. We evaluate the approach on a suite of continuous control benchmarks and show that it can achieve comparable performance to existing safe learning techniques while incurring fewer safety violations. Additionally, we present theoretical results showing that SPICE converges to the optimal safe policy under reasonable assumptions. 

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2. Dynamic Model Predictive Shielding for Provably Safe Reinforcement Learning

   Banerjee, Arko; Rahmani, Kia; Biswas, Joydeep; Dillig, Isil (December 2024, Neurips 2024)

   Among approaches for provably safe reinforcement learning, Model Predictive Shielding (MPS) has proven effective at complex tasks in continuous, high-dimensional state spaces, by leveraging a backup policy to ensure safety when the learned policy attempts to take risky actions. However, while MPS can ensure safety both during and after training, it often hinders task progress due to the conservative and task-oblivious nature of backup policies. This paper introduces Dynamic Model Predictive Shielding (DMPS), which optimizes reinforcement learning objectives while maintaining provable safety. DMPS employs a local planner to dynamically select safe recovery actions that maximize both short-term progress as well as long-term rewards. Crucially, the planner and the neural policy play a synergistic role in DMPS. When planning recovery actions for ensuring safety, the planner utilizes the neural policy to estimate long-term rewards, allowing it to observe beyond its short-term planning horizon. Conversely, the neural policy under training learns from the recovery plans proposed by the planner, converging to policies that are both high-performing and safe in practice. This approach guarantees safety during and after training, with bounded recovery regret that decreases exponentially with planning horizon depth. Experimental results demonstrate that DMPS converges to policies that rarely require shield interventions after training and achieve higher rewards compared to several state-of-the-art baselines 

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3. CAT: Closed-loop Adversarial Training for Safe End-to-End Driving

   Zhang, Linrui; Peng, Zhenghao; Li, Quanyi; Zhou, Bolei. (November 2023, Conference on Robot Learning (CoRL) 2023)

   Driving safety is a top priority for autonomous vehicles. Orthogonal to prior work handling accident-prone traffic events by algorithm designs at the policy level, we investigate a Closed-loop Adversarial Training (CAT) framework for safe end-to-end driving in this paper through the lens of environment augmentation. CAT aims to continuously improve the safety of driving agents by training the agent on safety-critical scenarios that are dynamically generated over time. A novel resampling technique is developed to turn log-replay real-world driving scenarios into safety-critical ones via probabilistic factorization, where the adversarial traffic generation is modeled as the multiplication of standard motion prediction sub-problems. Consequently, CAT can launch more efficient physical attacks compared to existing safety-critical scenario generation methods and yields a significantly less computational cost in the iterative learning pipeline. We incorporate CAT into the MetaDrive simulator and validate our approach on hundreds of driving scenarios imported from real-world driving datasets. Experimental results demonstrate that CAT can effectively generate adversarial scenarios countering the agent being trained. After training, the agent can achieve superior driving safety in both log-replay and safety-critical traffic scenarios on the held- out test set. Code and data are available at https://metadriverse.github.io/cat. 

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4. Safe adaptive output‐feedback optimal control of a class of linear systems

   https://doi.org/10.1002/rnc.7334  

   Mahmud, S_M Nahid; Abudia, Moad; Nivison, Scott A; Bell, Zachary I; Kamalapurkar, Rushikesh (July 2024, International Journal of Robust and Nonlinear Control)

   The objective of this research is to enable safety‐critical systems to simultaneously learn and execute optimal control policies in a safe manner to achieve complex autonomy. Learning optimal policies via trial and error, that is, traditional reinforcement learning, is difficult to implement in safety‐critical systems, particularly when task restarts are unavailable. Safe model‐based reinforcement learning techniques based on a barrier transformation have recently been developed to address this problem. However, these methods rely on full‐state feedback, limiting their usability in a real‐world environment. In this work, an output‐feedback safe model‐based reinforcement learning technique based on a novel barrier‐aware dynamic state estimator has been designed to address this issue. The developed approach facilitates simultaneous learning and execution of safe control policies for safety‐critical linear systems. Simulation results indicate that barrier transformation is an effective approach to achieve online reinforcement learning in safety‐critical systems using output feedback. 

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5. LeTO: Learning Constrained Visuomotor Policy With Differentiable Trajectory Optimization

   https://doi.org/10.1109/TASE.2024.3486542  

   Xu, Zhengtong; She, Yu (March 2025, IEEE Transactions on Automation Science and Engineering)

   This paper introduces LeTO, a method for learning constrained visuomotor policy with differentiable trajectory optimization. Our approach integrates a differentiable optimization layer into the neural network. By formulating the optimization layer as a trajectory optimization problem, we enable the model to end-to-end generate actions in a safe and constraint-controlled fashion without extra modules. Our method allows for the introduction of constraint information during the training process, thereby balancing the training objectives of satisfying constraints, smoothing the trajectories, and minimizing errors with demonstrations. This “gray box” method marries optimization-based safety and interpretability with powerful representational abilities of neural networks. We quantitatively evaluate LeTO in simulation and in the real robot. The results demonstrate that LeTO performs well in both simulated and real-world tasks. In addition, it is capable of generating trajectories that are less uncertain, higher quality, and smoother compared to existing imitation learning methods. Therefore, it is shown that LeTO provides a practical example of how to achieve the integration of neural networks with trajectory optimization. We release our code at https://github.com/ZhengtongXu/LeTO. 

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