Breaking safety constraints in control systems can lead to potential risks,
resulting in unexpected costs or catastrophic damage. Nevertheless, uncertainty
is ubiquitous, even among similar tasks. In this paper, we develop a novel
adaptive safe control framework that integrates meta learning, Bayesian models,
and control barrier function (CBF) method. Specifically, with the help of CBF
method, we learn the inherent and external uncertainties by a unified adaptive
Bayesian linear regression (ABLR) model, which consists of a forward neural
network (NN) and a Bayesian output layer. Meta learning techniques are
leveraged to pre-train the NN weights and priors of the ABLR model using data
collected from historical similar tasks. For a new control task, we refine the
meta-learned models using a few samples, and introduce pessimistic confidence
bounds into CBF constraints to ensure safe control. Moreover, we provide
theoretical criteria to guarantee probabilistic safety during the control
processes. To validate our approach, we conduct comparative experiments in
various obstacle avoidance scenarios. The results demonstrate that our
algorithm significantly improves the Bayesian model-based CBF method, and is
capable for efficient safe exploration even with multiple uncertain
constraints.

本文提出了一种新颖的自适应安全控制框架，该框架采用元学习、贝叶斯模型和控制障碍函数（CBF）方法，在多重不确定性条件下保证控制过程中的概率安全性。

模型辅助的基于概率的安全自适应控制与元贝叶斯学习

Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian  Learning

We study probabilistic safety for Bayesian Neural Networks (BNNs) under
adversarial input perturbations. Given a compact set of input points, $T
\subseteq \mathbb{R}^m$, we study the probability w.r.t. the BNN posterior that
all the points in $T$ are mapped to the same region $S$ in the output space. In
particular, this can be used to evaluate the probability that a network sampled
from the BNN is vulnerable to adversarial attacks. We rely on relaxation
techniques from non-convex optimization to develop a method for computing a
lower bound on probabilistic safety for BNNs, deriving explicit procedures for
the case of interval and linear function propagation techniques. We apply our
methods to BNNs trained on a regression task, airborne collision avoidance, and
MNIST, empirically showing that our approach allows one to certify
probabilistic safety of BNNs with millions of parameters.

研究了在敌对输入扰动下，贝叶斯神经网络的概率安全性，使用非凸优化松弛技术计算贝叶斯神经网络概率安全性的下界，并且证明方法可用于对具有数百万参数的 BNN 进行概率安全性的认证。