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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 1 (Introduction to OT, Multi Marginal OT and entropic OT)
- OT, its CFD (kinetic energy) interpretation and their Kantorovich (optimisation in measure space) relaxation.
- Time discretisation and Multi Marginal OT.
- Entropic regularisation and Sinkhorn.
- Shortlist of problem addressed in the lecture series.