  Asymmetrical distance structures (quasimetrics) are ubiquitous in our lives
and are gaining more attention in machine learning applications. Imposing such
quasimetric structures in model representations has been shown to improve many
tasks, including reinforcement learning (RL) and causal relation learning. In
this work, we present four desirable properties in such quasimetric models, and
show how prior works fail at them. We propose Interval Quasimetric Embedding
(IQE), which is designed to satisfy all four criteria. On three quasimetric
learning experiments, IQEs show strong approximation and generalization
abilities, leading to better performance and improved efficiency over prior
methods.
  Project Page: https://www.tongzhouwang.info/interval_quasimetric_embedding
  Quasimetric Learning Code Package:
https://www.github.com/quasimetric-learning/torch-quasimetric
