This paper presents an adaptive online learning framework for systems with
uncertain parameters to ensure safety-critical control in non-stationary
environments. Our approach consists of two phases. The initial phase is
centered on a novel sparse Gaussian process (GP) framework. We first integrate
a forgetting factor to refine a variational sparse GP algorithm, thus enhancing
its adaptability. Subsequently, the hyperparameters of the Gaussian model are
trained with a specially compound kernel, and the Gaussian model's online
inferential capability and computational efficiency are strengthened by
updating a solitary inducing point derived from new samples, in conjunction
with the learned hyperparameters. In the second phase, we propose a safety
filter based on high-order control barrier functions (HOCBFs), synergized with
the previously trained learning model. By leveraging the compound kernel from
the first phase, we effectively address the inherent limitations of GPs in
handling high-dimensional problems for real-time applications. The derived
controller ensures a rigorous lower bound on the probability of satisfying the
safety specification. Finally, the efficacy of our proposed algorithm is
demonstrated through real-time obstacle avoidance experiments executed using
both a simulation platform and a real-world 7-DOF robot.

本文提出了一种适应不确定参数系统的自适应在线学习框架，以确保非平稳环境下的安全临界控制；该方法包括两个阶段，第一阶段基于稀疏高斯过程算法改进，第二阶段提出了基于高阶控制屏障函数的安全过滤器与学习模型相结合，并通过实时障碍物避免实验证明了算法的有效性。

高阶不确定模型中的实时自适应安全关键控制与高斯过程

Real-Time Adaptive Safety-Critical Control with Gaussian Processes in  High-Order Uncertain Models

Online learning is not always about memorizing everything. Since the future
can be statistically very different from the past, a critical challenge is to
gracefully forget the history while new data comes in. To formalize this
intuition, we revisit the classical notion of discounted regret using recently
developed techniques in adaptive online learning. Our main result is a new
algorithm that adapts to the complexity of both the loss sequence and the
comparator, improving the widespread non-adaptive algorithm - gradient descent
with a constant learning rate. In particular, our theoretical guarantee does
not require any structural assumption beyond convexity, and the algorithm is
provably robust to suboptimal hyperparameter tuning. We further demonstrate
such benefits through online conformal prediction, a downstream online learning
task with set-membership decisions.

在线学习不仅仅是记住一切。通过使用自适应在线学习中近期开发的技术重新审视折扣遗憾的经典概念，我们提出了一个能够优雅地在新数据到达时遗忘历史的关键算法，改进了传统的非自适应算法，即使用固定学习率的梯度下降算法。具体而言，我们的理论保证不需要任何除了凸性之外的结构假设，该算法在次优超参数调整时可以证明是鲁棒的。通过在线符合预测，我们进一步展示了这些好处，它是一个具有集合成员决策的下游在线学习任务。