This course will cover some state-of-the-art applications of modern computational optimal transport using entropic regularisation. We will start with a brief introduction to optimal transport and entropic regularisation before discussing three topics in more detail: second order mean field games, Arnold’s Euler geodesics, and semi-martingale optimal transport.
Lecture 3 (Generalised Euler geodesics as Multi Marginal OT)
- Intro to Arnold’s Euler geodesics.
- Brenier relaxation 1 : Lagrangian discretisation and solutions.
- Brenier relaxation 2 : Eulerian formulation and MMOT and Entropic approximation via Sinkhorn.