  What is a good exploration strategy for an agent that interacts with an
environment in the absence of external rewards? Ideally, we would like to get a
policy driving towards a uniform state-action visitation (highly exploring) in
a minimum number of steps (fast mixing), in order to ease efficient learning of
any goal-conditioned policy later on. Unfortunately, it is remarkably arduous
to directly learn an optimal policy of this nature. In this paper, we propose a
novel surrogate objective for learning highly exploring and fast mixing
policies, which focuses on maximizing a lower bound to the entropy of the
steady-state distribution induced by the policy. In particular, we introduce
three novel lower bounds, that lead to as many optimization problems, that
tradeoff the theoretical guarantees with computational complexity. Then, we
present a model-based reinforcement learning algorithm, IDE$^{3}$AL, to learn
an optimal policy according to the introduced objective. Finally, we provide an
empirical evaluation of this algorithm on a set of hard-exploration tasks.
