  In this paper, we derive a novel method as a generalization over LCEs such as
E2C. The method develops the idea of learning a locally linear state space, by
adding a multi-step prediction, thus allowing for more explicit control over
the curvature. We show, that the method outperforms E2C without drastic model
changes which come with other works, such as PCC and P3C. We discuss the
relation between E2C and the presented method and derived update equations. We
provide empirical evidence, which suggests that by considering the multi-step
prediction our method - ms-E2C - allows to learn much better latent state
spaces in terms of curvature and next state predictability. Finally, we also
discuss certain stability challenges we encounter with multi-step predictions
and the ways to mitigate them.
