ICML Tutorial 2023

Speakers: Charlotte Bunne (ETH Zurich) and Marco Cuturi (ENSAE CREST and Apple)

Optimal Transport in Learning, Control, and Dynamical Systems

Over the last decade, optimal transport (OT) has evolved from a prize-winning research area in pure mathematics to a recurring theme bursting repeatedly across all machine learning areas. OT, both through its theory and computations, has enabled breakthroughs using a multi-pronged approach, blending elements from convex optimization (e.g., linear and quadratic assignment problems, the Sinkhorn algorithm), analysis (partial differential equations (PDE), links to Monge-Ampère equation), stochastic calculus (diffusion models, Schrödinger bridge), statistics (analysis of sampling algorithms, generalized quantiles, generative model fitting), and deep architectures. Because many of these developments have happened in parallel, the field is increasingly difficult and diverse to grasp for a non-informed audience. The goal of this tutorial will be to provide a unifying perspective that underlines the centrality of OT to the wealth of developments listed above, drawing connections between these approaches both in algorithms and theory, and provide some directions on how the field can further evolve to create new ML methods grounded on this exciting toolbox.

Part 1: From Optimal Matchings to Monge, Kantorovich and Gromov Problems, Sinkhorn, and other Regularized Estimators

Part 2: Tackling the Monge Problem with the Brenier Theorem

Part 3: Modeling Measure Dynamics with Optimal Transport