Motion Planning for Identification of Linear Classifiers

A given region in 2-D Euclidean space is divided by a unknown linear classifier in to two sets each carrying a label. The objective of an agent with known dynamics traversing the region is to identify the true classifier while paying a control cost across its trajectory. We consider two scenarios: (i) the agent is able to measure the true label perfectly; (ii) the observed label is the true label multiplied by noise. We present the following: (i) the classifier identification problem formulated as a control problem; (ii) geometric interpretation of the control problem resulting in one step modified control problems; (iii) control algorithms that result in data sets which are used to identify the true classifier with accuracy; (iv) convergence of estimated classifier to the true classifier when the observed label is not corrupted by noise; (iv) numerical example demonstrating the utility of the control algorithms.