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

Improved Representation of Asymmetrical Distances with Interval Quasimetric Embeddings