  This paper studies directed exploration for reinforcement learning agents by
tracking uncertainty about the value of each available action. We identify two
sources of uncertainty that are relevant for exploration. The first originates
from limited data (parametric uncertainty), while the second originates from
the distribution of the returns (return uncertainty). We identify methods to
learn these distributions with deep neural networks, where we estimate
parametric uncertainty with Bayesian drop-out, while return uncertainty is
propagated through the Bellman equation as a Gaussian distribution. Then, we
identify that both can be jointly estimated in one network, which we call the
Double Uncertain Value Network. The policy is directly derived from the learned
distributions based on Thompson sampling. Experimental results show that both
types of uncertainty may vastly improve learning in domains with a strong
exploration challenge.
