Towards Better Laplacian Representation in Reinforcement Learning with Generalized Graph Drawing

Understand

The Laplacian representation recently gains increasing attention for reinforcement learning as it provides succinct and informative representation for states, by taking the eigenvectors of the Laplacian matrix of the state-transition graph as state embeddings.

• Such representation captures the geometry of the underlying state space and is beneficial to RL tasks such as option discovery and reward shaping.
• To approximate the Laplacian representation in large (or even continuous) state spaces, recent works propose to minimize a spectral graph drawing objective, which however has infinitely many global minimizers other than the eigenvectors.
• As a result, their learned Laplacian representation may differ from the ground truth.