Stochastic optimization for large scale optimal transport

A university project about Stochastic Optimal Transport

Description

This project was part of the course Mathematical Foundations Of Data Science taught by Gabriel Peyré in 2019.

The goal was to reproduce and extend results from [1] to other optimization algorithms, including SAGA [2]. After comparing the regularized optimal transport convergence results for these algorithms, I studied an optimal school placement and allocation problem in several French regions.


References

  1. Genevay, A., Cuturi, M., Peyré, G. & Bach, F.. Stochastic Optimization for Large-scale Optimal Transport. in Advances in Neural Information Processing Systems 29 (eds. Lee, D. D., Sugiyama, M., Luxburg, U. V., Guyon, I. & Garnett, R.) 3440–3448 (2016).
  2. Defazio, A., Bach, F. & Lacoste-Julien, S.. SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives. arXiv:1407.0202 [cs, math, stat] (2014).