We present an optimal transport framework for learning topics from textual data. While the celebrated Latent Dirichlet allocation (LDA) topic model and its variants have been applied to many disciplines, they mainly focus on wordoccurrences and neglect to incorporate semantic regularities in language.

For deterministic feedback, we additionally present a gap-independent algorithm that identifies a Condorcet winning team withinO(nklog(k)+k5)duels.