Transport Optimal (OPT) is a mathematical theory and computational framework used to study the movement of mass (or distributions) in a way that minimizes the cost associated with transporting that mass from one location to another. Originally developed in the early 20th century, this concept has gained significant traction in various fields, especially in apprentissage automatique, vision par ordinateur, and statistics.
At its core, Optimal Transport seeks to find the most efficient way to transform one probability distribution into another. This is often visualized as moving ‘mass’ from one shape (distribution) to another while minimizing the total cost of transportation. The cost can be defined in various ways, such as the Distance Euclidienne between points in space. The theory provides a robust mathematical foundation for comparing distributions, enabling applications such as adaptation de domaine, morphing d'images, and generative modeling.
In the context of AI and machine learning, OPT has been utilized in various algorithms to improve tasks such as classification d'image, object detection, and generative adversarial networks (GANs). By allowing for a more nuanced understanding of the differences between distributions, Optimal Transport can yield superior results in tasks that involve comparing data sets or generating new data that closely resembles a training set.
De plus, de nombreuses méthodes computationnelles, telles que la distance de Sinkhorn, ont été développées pour rendre la mise en œuvre du Transport Optimal plus réalisable en pratique, permettant le calcul efficace des plans de transport même pour des problèmes à grande échelle.