Learning time-series models is useful for many applications, such as
simulation and forecasting. In this study, we consider the problem of actively
learning time-series models while taking given safety constraints into account.
For time-series modeling we employ a Gaussian process with a nonlinear
exogenous input structure. The proposed approach generates data appropriate for
time series model learning, i.e. input and output trajectories, by dynamically
exploring the input space. The approach parametrizes the input trajectory as
consecutive trajectory sections, which are determined stepwise given safety
requirements and past observations. We analyze the proposed algorithm and
evaluate it empirically on a technical application. The results show the
effectiveness of our approach in a realistic technical use case.

通过使用高斯过程和非线性外部输入结构在考虑给定安全约束条件的情况下，活跃地学习时间序列模型，使用动态探索输入空间生成适用于时间序列模型学习的数据，然后通过逐步确定安全要求和过去观察结果来对输入轨迹进行参数化分析，并在技术应用中进行实证评估，结果显示我们的方法在现实技术用例中的有效性。

基于高斯过程的安全主动学习用于时间序列建模

Safe Active Learning for Time-Series Modeling with Gaussian Processes

In this paper, we investigate a problem of actively learning threshold in
latent space, where the unknown reward $g(\gamma, v)$ depends on the proposed
threshold $\gamma$ and latent value $v$ and it can be $only$ achieved if the
threshold is lower than or equal to the unknown latent value. This problem has
broad applications in practical scenarios, e.g., reserve price optimization in
online auctions, online task assignments in crowdsourcing, setting recruiting
bars in hiring, etc. We first characterize the query complexity of learning a
threshold with the expected reward at most $\epsilon$ smaller than the optimum
and prove that the number of queries needed can be infinitely large even when
$g(\gamma, v)$ is monotone with respect to both $\gamma$ and $v$. On the
positive side, we provide a tight query complexity
$\tilde{\Theta}(1/\epsilon^3)$ when $g$ is monotone and the CDF of value
distribution is Lipschitz. Moreover, we show a tight
$\tilde{\Theta}(1/\epsilon^3)$ query complexity can be achieved as long as $g$
satisfies one-sided Lipschitzness, which provides a complete characterization
for this problem. Finally, we extend this model to an online learning setting
and demonstrate a tight $\Theta(T^{2/3})$ regret bound using continuous-arm
bandit techniques and the aforementioned query complexity results.

主要研究领域包括主动学习、阈值、潜在空间和查询复杂度，通过研究阈值的学习和潜在值的奖励函数，提供了对于问题的完整描述并给出了其查询复杂度的紧密上界和下界。此外，还将该模型扩展到在线学习领域，并使用连续臂赌博技术和查询复杂度结果证明了紧密的遗憾界。