  We study the problem of predicting and controlling the future state
distribution of an autonomous agent. This problem, which can be viewed as a
reframing of goal-conditioned reinforcement learning (RL), is centered around
learning a conditional probability density function over future states. Instead
of directly estimating this density function, we indirectly estimate this
density function by training a classifier to predict whether an observation
comes from the future. Via Bayes' rule, predictions from our classifier can be
transformed into predictions over future states. Importantly, an off-policy
variant of our algorithm allows us to predict the future state distribution of
a new policy, without collecting new experience. This variant allows us to
optimize functionals of a policy's future state distribution, such as the
density of reaching a particular goal state. While conceptually similar to
Q-learning, our work lays a principled foundation for goal-conditioned RL as
density estimation, providing justification for goal-conditioned methods used
in prior work. This foundation makes hypotheses about Q-learning, including the
optimal goal-sampling ratio, which we confirm experimentally. Moreover, our
proposed method is competitive with prior goal-conditioned RL methods.
