  Goal-conditioned planning benefits from learned low-dimensional
representations of rich observations. While compact latent representations
typically learned from variational autoencoders or inverse dynamics enable
goal-conditioned decision making, they ignore state reachability, hampering
their performance. In this paper, we learn a representation that associates
reachable states together for effective planning and goal-conditioned policy
learning. We first learn a latent representation with multi-step inverse
dynamics (to remove distracting information), and then transform this
representation to associate reachable states together in $\ell_2$ space. Our
proposals are rigorously tested in various simulation testbeds. Numerical
results in reward-based settings show significant improvements in sampling
efficiency. Further, in reward-free settings this approach yields layered state
abstractions that enable computationally efficient hierarchical planning for
reaching ad hoc goals with zero additional samples.
