  High-dimensional observations and unknown dynamics are major challenges when
applying optimal control to many real-world decision making tasks. The Learning
Controllable Embedding (LCE) framework addresses these challenges by embedding
the observations into a lower dimensional latent space, estimating the latent
dynamics, and then performing control directly in the latent space. To ensure
the learned latent dynamics are predictive of next-observations, all existing
LCE approaches decode back into the observation space and explicitly perform
next-observation prediction---a challenging high-dimensional task that
furthermore introduces a large number of nuisance parameters (i.e., the
decoder) which are discarded during control. In this paper, we propose a novel
information-theoretic LCE approach and show theoretically that explicit
next-observation prediction can be replaced with predictive coding. We then use
predictive coding to develop a decoder-free LCE model whose latent dynamics are
amenable to locally-linear control. Extensive experiments on benchmark tasks
show that our model reliably learns a controllable latent space that leads to
superior performance when compared with state-of-the-art LCE baselines.
