tutorials

Foundations 0/2

The transport problem itself, and the distance it induces. Expands Background in the survey.

1. Monge, Kantorovich and Benamou-Brenier planned Three ways to state the same transport problem, and why each one is useful.
2. The Wasserstein Distance planned What the transport cost measures, and how its geometry differs from other divergences.

Computational Optimal Transport 1/6

How transport problems are actually solved at scale. Expands Computational Optimal Transport in the survey.

1. Entropic Regularization and Sinkhorn planned Trading exactness for speed, and what the regularization does to the transport plan.
2. The Sliced Wasserstein Distance Projecting to one dimension, where transport is a sort — and what that costs you in bias.
3. Gromov-Wasserstein and Incomparable Spaces planned Comparing distributions that do not live in the same space at all.
4. Neural Network Solvers planned Input-convex networks and learning the transport map instead of solving for it.
5. Mini-batch Optimal Transport planned What happens to a transport plan when you only ever see a batch at a time.
6. Partial, Unbalanced and Weak Optimal Transport planned Relaxing the constraint that all mass must move, and why outliers stop mattering.

Supervised Learning 0/2

Transport costs as training objectives, and as a lens on fairness. Expands Supervised Learning in the survey.

1. Optimal Transport as a Loss planned Using a transport cost where a cross-entropy would normally go.
2. Transport and Fairness planned Repairing a representation by transporting groups onto a common barycenter.

Unsupervised Learning 0/3

Generating, decomposing and grouping data through transport. Expands Unsupervised Learning in the survey.

1. Generative Modelling planned Where the Wasserstein distance enters GANs, VAEs and adversarial autoencoders.
2. Wasserstein Dictionary Learning planned Decomposing a dataset into atoms that are themselves distributions.
3. Clustering planned k-means as a transport problem, and what barycenters buy you.

Transfer Learning 0/3

Moving models across domains — the corner of the field this series' author works in. Expands Transfer Learning in the survey.

1. Shallow Domain Adaptation planned Transporting source samples onto the target distribution, and regularizing by class.
2. Deep Domain Adaptation planned Matching distributions in a learned latent space rather than in input space.
3. Multi-Source Domain Adaptation planned Many sources, one target, and the barycenter that sits between them.

Reinforcement Learning 0/2

Distributions over returns, and transport in policy optimization. Expands Reinforcement Learning in the survey.

1. Distributional Reinforcement Learning planned Learning the whole return distribution, and measuring it with a Wasserstein metric.
2. Bayesian RL and Policy Optimization planned Transport as a trust region on the space of policies.

Where This Leaves Us 0/1

What is still hard, and what looks promising. Expands Final Remarks in the survey.

1. Challenges and Open Problems planned Sample complexity, the curse of dimensionality, and where the estimators break down.