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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 2 (Second Order Mean Field Games as Entropic Multi Marginal OT)
- The Schroedinger problem, static versus dynamic formulations.
- Extension to second order Mean Field Games.
- Application of Multi Marginal Sinkhorn algorithms to solve them.