Gathering the most information by picking the least amount of data is a common task in experimental design or when exploring an unknown environment in reinforcement learning and robotics. A widely used measure for quantifying the information contained in some distribution of interest is its entropy. Greedily minimizing the expected entropy is therefore a standard method for choosing samples in order to gain strong beliefs about the underlying random variables. We show that this approach is prone to temporally getting stuck in local optima corresponding to wrongly biased beliefs. We suggest instead maximizing the expected cross entropy between old and new belief, which aims at challenging refutable beliefs and thereby avoids these local optima. We show that both criteria are closely related and that their dierence can be traced back to the asymmetry of the Kullback-Leibler divergence. In illustrative examples as well as simulated and real-world experiments we demonstrate the advantage of cross entropy over simple entropy for practical applications.
We introduce a particle filter-based approach to representing and actively reducing uncertainty over articulated motion models. The presented method provides a probabilistic model that integrates visual observations with feedback from manipulation actions to best characterize a distribution of possible articulation models. We evaluate several action selection methods to efficiently reduce the uncertainty about the articulation model. The full system is experimentally evaluated using a PR2 mobile manipulator. Our experiments demonstrate that the proposed system allows for intelligent reasoning about sparse, noisy data in a number of common manipulation scenarios.