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