Data selection for multi-task learning under dynamic constraints

Learning-based techniques are increasingly effective at controlling complex systems using data-driven models. However, most work done so far has focused on learning individual tasks or control laws. Hence, it is still a largely unaddressed research question how multiple tasks can be learned efficiently and simultaneously on the same system. In particular, no efficient state space exploration schemes have been designed for multi-task control settings. Using this research gap as our main motivation, we present an algorithm that approximates the smallest data set that needs to be collected in order to achieve high control performance for multiple learning-based control laws. We describe system uncertainty using a probabilistic Gaussian process model, which allows us to quantify the impact of potentially collected data on each learning-based controller. We then determine the optimal measurement locations by solving a stochastic optimization problem approximately. We show that, under reasonable assumptions, the approximate solution converges towards that of the exact problem. Additionally, we provide a numerical illustration of the proposed algorithm.