  Learning the dynamics of a physical system wherein an autonomous agent
operates is an important task. Often these systems present apparent geometric
structures. For instance, the trajectories of a robotic manipulator can be
broken down into a collection of its transitional and rotational motions, fully
characterized by the corresponding Lie groups and Lie algebras. In this work,
we take advantage of these structures to build effective dynamical models that
are amenable to sample-based learning. We hypothesize that learning the
dynamics on a Lie algebra vector space is more effective than learning a direct
state transition model. To verify this hypothesis, we introduce the Group
Enhanced Model (GEM). GEMs significantly outperform conventional transition
models on tasks of long-term prediction, planning, and model-based
reinforcement learning across a diverse suite of standard continuous-control
environments, including Walker, Hopper, Reacher, Half-Cheetah, Inverted
Pendulums, Ant, and Humanoid. Furthermore, plugging GEM into existing state of
the art systems enhances their performance, which we demonstrate on the PETS
system. This work sheds light on a connection between learning of dynamics and
Lie group properties, which opens doors for new research directions and
practical applications along this direction. Our code is publicly available at:
https://tinyurl.com/GEMMBRL.
