  Stability is a basic requirement when studying the behavior of dynamical
systems. However, stabilizing dynamical systems via reinforcement learning is
challenging because only little data can be collected over short time horizons
before instabilities are triggered and data become meaningless. This work
introduces a reinforcement learning approach that is formulated over latent
manifolds of unstable dynamics so that stabilizing policies can be trained from
few data samples. The unstable manifolds are minimal in the sense that they
contain the lowest dimensional dynamics that are necessary for learning
policies that guarantee stabilization. This is in stark contrast to generic
latent manifolds that aim to approximate all -- stable and unstable -- system
dynamics and thus are higher dimensional and often require higher amounts of
data. Experiments demonstrate that the proposed approach stabilizes even
complex physical systems from few data samples for which other methods that
operate either directly in the system state space or on generic latent
manifolds fail.
