Exploring every possibility and training a model for each is impractical.

Focusing learning on these relevant actions can significantly improve training efficiency and effectiveness.

The deployment of autonomous robots in safety-critical applications requires safety guarantees. Provably safe reinforcement learning is an active field of research that aims to provide such guarantees using safeguards. These safeguards should be integrated during training to reduce the sim-to-real gap. While there are several approaches for safeguarding sampling-based reinforcement learning, analytic gradient-based reinforcement learning often achieves superior performance from fewer environment interactions. However, there is no safeguarding approach for this learning paradigm yet. Our work addresses this gap by developing the first effective safeguard for analytic gradient-based reinforcement learning. We analyse existing, differentiable safeguards, adapt them through modified mappings and gradient formulations, and integrate them into a state-of-the-art learning algorithm and a differentiable simulation. Using numerical experiments on three control tasks, we evaluate how different safeguards affect learning. The results demonstrate safeguarded training without compromising performance.

Abstract-- Predicting the motion of surrounding vehicles is key to safe autonomous driving, especially in unstructured environments without prior information. This paper proposes a novel online method to accurately predict the occupancy sets of surrounding vehicles based solely on motion observations. The approach is divided into two stages: first, an Extended Kalman Filter and a Linear Programming (LP) problem are used to estimate a compact zonotopic set of control actions; then, a reachability analysis propagates this set to predict future occupancy. The effectiveness of the method has been validated through simulations in an urban environment, showing accurate and compact predictions without relying on prior assumptions or prior training data. I. INTRODUCTION Autonomous driving has generated great research interests given the expected benefits, such as reducing accidents, optimizing traffic efficiency and energy management [1]. However, ensuring safety remains a major challenge, particularly in urban environments, where multiple agents interact dynamically [2].Predicting the motion of surrounding vehicles (SVs) is critical to designing safe motion planning and control strategies for autonomous vehicles.

Focusing learning on these relevant actions can significantly improve training efficiency and effectiveness.

Exploring every possibility and training a model for each is impractical.

Neural networks with ReLU activations are a widely used model in machine learning. It is thus important to have a profound understanding of the properties of the functions computed by such networks. Recently, there has been increasing interest in the (parameterized) computational complexity of determining these properties. In this work, we close several gaps and resolve an open problem posted by Froese et al. [COLT '25] regarding the parameterized complexity of various problems related to network verification. In particular, we prove that deciding positivity (and thus surjectivity) of a function $f\colon\mathbb{R}^d\to\mathbb{R}$ computed by a 2-layer ReLU network is W[1]-hard when parameterized by $d$. This result also implies that zonotope (non-)containment is W[1]-hard with respect to $d$, a problem that is of independent interest in computational geometry, control theory, and robotics. Moreover, we show that approximating the maximum within any multiplicative factor in 2-layer ReLU networks, computing the $L_p$-Lipschitz constant for $p\in(0,\infty]$ in 2-layer networks, and approximating the $L_p$-Lipschitz constant in 3-layer networks are NP-hard and W[1]-hard with respect to $d$. Notably, our hardness results are the strongest known so far and imply that the naive enumeration-based methods for solving these fundamental problems are all essentially optimal under the Exponential Time Hypothesis.