  Goal-conditioned reinforcement learning (RL) is an interesting extension of
the traditional RL framework, where the dynamic environment and reward sparsity
can cause conventional learning algorithms to fail. Reward shaping is a
practical approach to improving sample efficiency by embedding human domain
knowledge into the learning process. Existing reward shaping methods for
goal-conditioned RL are typically built on distance metrics with a linear and
isotropic distribution, which may fail to provide sufficient information about
the ever-changing environment with high complexity. This paper proposes a novel
magnetic field-based reward shaping (MFRS) method for goal-conditioned RL tasks
with dynamic target and obstacles. Inspired by the physical properties of
magnets, we consider the target and obstacles as permanent magnets and
establish the reward function according to the intensity values of the magnetic
field generated by these magnets. The nonlinear and anisotropic distribution of
the magnetic field intensity can provide more accessible and conducive
information about the optimization landscape, thus introducing a more
sophisticated magnetic reward compared to the distance-based setting. Further,
we transform our magnetic reward to the form of potential-based reward shaping
by learning a secondary potential function concurrently to ensure the optimal
policy invariance of our method. Experiments results in both simulated and
real-world robotic manipulation tasks demonstrate that MFRS outperforms
relevant existing methods and effectively improves the sample efficiency of RL
algorithms in goal-conditioned tasks with various dynamics of the target and
obstacles.
