  We propose a novel way to integrate control techniques with reinforcement
learning (RL) for stability, robustness, and generalization: leveraging
contraction theory to realize modularity in neural control, which ensures that
combining stable subsystems can automatically preserve the stability. We
realize such modularity via signal composition and dynamic decomposition.
Signal composition creates the latent space, within which RL applies to
maximizing rewards. Dynamic decomposition is realized by coordinate
transformation that creates an auxiliary space, within which the latent signals
are coupled in the way that their combination can preserve stability provided
each signal, that is, each subsystem, has stable self-feedbacks. Leveraging
modularity, the nonlinear stability problem is deconstructed into algebraically
solvable ones, the stability of the subsystems in the auxiliary space, yielding
linear constraints on the input gradients of control networks that can be as
simple as switching the signs of network weights. This minimally invasive
method for stability allows arguably easy integration into the modular neural
architectures in machine learning, like hierarchical RL, and improves their
performance. We demonstrate in simulation the necessity and the effectiveness
of our method: the necessity for robustness and generalization, and the
effectiveness in improving hierarchical RL for manipulation learning.
