Learning-based methods have been successful in solving complex control tasks
without significant prior knowledge about the system. However, these methods
typically do not provide any safety guarantees, which prevents their use in
safety-critical, real-world applications. In this paper, we present a
learning-based model predictive control scheme that can provide provable
high-probability safety guarantees. To this end, we exploit regularity
assumptions on the dynamics in terms of a Gaussian process prior to construct
provably accurate confidence intervals on predicted trajectories. Unlike
previous approaches, we do not assume that model uncertainties are independent.
Based on these predictions, we guarantee that trajectories satisfy safety
constraints. Moreover, we use a terminal set constraint to recursively
guarantee the existence of safe control actions at every iteration. In our
experiments, we show that the resulting algorithm can be used to safely and
efficiently explore and learn about dynamic systems.

本文提出了一种基于学习的模型预测控制方案，其可以提供可证明的高概率安全保证，并利用正态分布先验的规则性假设来构建可证明准确的置信区间，保证轨迹满足安全约束，通过终端集约束递归地保证每个迭代中存在安全控制动作。在实验中展现了该算法可以用来安全、高效地探索和学习动态系统。

基于学习的模型预测控制用于安全探索

Learning-based Model Predictive Control for Safe Exploration

Neural networks have been widely used to solve complex real-world problems.
Due to the complicate, nonlinear, non-convex nature of neural networks, formal
safety guarantees for the output behaviors of neural networks will be crucial
for their applications in safety-critical systems.In this paper, the output
reachable set computation and safety verification problems for a class of
neural networks consisting of Rectified Linear Unit (ReLU) activation functions
are addressed. A layer-by-layer approach is developed to compute output
reachable set. The computation is formulated in the form of a set of
manipulations for a union of polyhedra, which can be efficiently applied with
the aid of polyhedron computation tools. Based on the output reachable set
computation results, the safety verification for a ReLU neural network can be
performed by checking the intersections of unsafe regions and output reachable
set described by a union of polyhedra. A numerical example of a randomly
generated ReLU neural network is provided to show the effectiveness of the
approach developed in this paper.

该论文探讨了一类由 ReLU 激活函数构成的神经网络的输出可达集计算和安全验证问题，并提出了一种逐层计算输出可达集的方法，通过计算输出可达集的结果，可以通过检查不安全区域与由一组多面体描述的输出可达集的交集来执行简单有效的安全验证。