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 4 (Entropic Semi-Martingale OT) 

  1. Martingale and Semi-Martingale OT. 
  2. Entropic Multi-Marginal OT version using the `specific relative entropy’. 
  3. Sinkhorn solutions.

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