Data Selection for Multi-Task Learning under Dynamic Constraints

Learning-based techniques are increasingly effective at controlling complex systems. However, most work done so far has focused on learning control laws for individual tasks. Simultaneously learning multiple tasks on the same system is still a largely unaddressed research question. 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 performance across multiple control tasks. By describing system uncertainty using a probabilistic Gaussian process model, we are able to quantify the impact of potentially collected data on each learning-based control law. 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 the exact one. Additionally, we provide a numerical illustration of the proposed algorithm.