  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 difference 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.
