CS 2840 is a graduate-level course on the mathematical foundations and computational practice of optimal transport, with a focus on its applications across modern machine learning.
Optimal transport (OT) studies how to move mass from one distribution to another at minimum cost — a problem with roots in 18th-century engineering that has, in the last decade, become a central tool in machine learning. This course covers the mathematics of OT (the Monge and Kantorovich formulations, Wasserstein distances, duality, dynamic formulations), its efficient computation (entropic regularization, Sinkhorn's algorithm, sliced and low-rank variants, neural estimators), and a wide range of applications: generative modeling, domain adaptation, graph representation learning, LLM alignment, and more.
The course is organized into four parts:
See the lecture navigator for the full schedule and the slides from each session.
Harvard SEAS · Fall 2025 · instructor David Alvarez-Melis. TFs: Alexandru (Alex) Meterez and Jaeyeon (Jay) Kim. The course met twice weekly from September 2 through November 20, 2025.
The full written syllabus — prerequisites, grading, policies, and references — is below.