Optimal Adaptive Sampling for Boundary Estimation with Mobile Sensors

We consider the problem of active learning in the context of spatial sampling for boundary estimation, where the goal is to estimate an unknown boundary as accurately and quickly as possible. We present a finite-horizon search procedure to optimally minimize both the final estimation error and the distance traveled for a fixed number of samples, where a tuning parameter is used to trade off between the estimation accuracy and distance traveled. We show that the resulting optimization problem can be solved in closed form and that the resulting policy generalizes existing approaches to this problem.