From Cone Geometry to Monge Structure: Local Defects and Global Regret in High-Dimensional Optimal Transport
The episode discusses the paper "From Cone Geometry to Monge Structure" which introduces a new structural route for high-dimensional optimal transport. The authors detail how using cone-compatible Monge geometry and specific objectives, such as Directed Cone OT, allows researchers to achieve exact, analytic solutions when data possesses an inherent directional flow. This approach moves beyond finding simple approximations.