The Advantage of Cross Entropy over Entropy in Iterative Information Gathering
This addresses a fundamental issue in sample selection for researchers and practitioners in fields like robotics and experimental design, offering an incremental improvement over existing methods.
The paper tackles the problem of iterative information gathering in experimental design and reinforcement learning, showing that the standard method of greedily minimizing expected entropy can get stuck in local optima due to biased beliefs, and instead proposes maximizing expected cross entropy to avoid these issues, demonstrating its advantage in simulated and real-world experiments.
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.