Paper:
Safe Active Learning for Time-Series Modeling with Gaussian Processes
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.

Review:
This paper proposes safe active learning algorithm for learning time-series models with piecewise trajectory sections. The basic model for the trajectory section is Gaussian Process, and the safety criterion is modeled as probability of certain safe value, which is modeled as a continuous function of inputs, being in the right region is greater than some threshold. The active learner explores the input space by generating trajectories that maximizes certain criterion in system identification. The paper also provides theoretical analysis in the safety perspective, as well as in the predictive variance reduction perspective. In the evaluation, besides simulated examples on predefined continuous functions and low dimensional models, this paper provides a specific use case for learning surrogate model of the high-pressure fluid system.   Significance The active learning here is not based on pool of data or stream of data. This work is more of active generation of the piecewise input trajectory in order to learn system property models while receiving output from the physical system and keeping the generation in the safety region. Safe exploration in the same flavor I believe has been studied before in regression when there is some hard threshold. This paper generally makes good contribution to safe active learning in system identification.  My concern though is that this work is not general enough for time series data. It mainly focuses on learning system models for physical systems. We need to have a good model for piecewise trajectory generation, we need to have continuous safety value function, and we need to have efficient optimization method for maximizing the optimality criteria when exploring. Therefore, my general suggestion here is to summarize all the conditions clearly in the paper for efficiently applying the method in practice.  Quality I have several questions which I wish could be answered to help me better judge the quality of the paper:  1. There is this constrained optimization problem that needed to be solved for every iteration of exploration. And there is several different criteria mentioned. But I did not find anything about how to solve the problem efficiently. Also, in evaluation, example 2 does not solve the optimization problem while in the use case is not clearly mentioned what criteria is used there.  2. Instead of using some hard threshold as safety criterion, the probability based safety criterion in this paper seems just a little softer. What is the consideration here?   3. There are actually many small hyperparameters needed to be set beforehand for this method. For example, the length of the initialization trajectories and the timestep in each trajectory section. There is no discussion about these in the paper. Both 10 and 25 are used in different experiments. I want to know what is the general principle of choosing them.  Originality This work reminds me of a previous thread of work on safe exploration based also on GP, but not on time series (like Safe Exploration for Optimization with Gaussian Processes), which is not cited in this paper. I think more discussion in related work may be needed.   Clarity The paper is generally well-written with clear presentation and examples.