6 papers
Oriented point-cloud varifolds for estimating the perimeter and computing its Wasserstein gradient flow
Tokuhiro Eto, Noboru Isobe
This paper develops a mesh-free numerical method for the one-phase Mullins-Sekerka flow, in which the interface bounding a set moves as the Wasserstein gradient flow of its perimet…
Minimax Optimal Estimation of Transport-Growth Pairs in Unbalanced Optimal Transport
Donlapark Ponnoprat, Noboru Isobe, Masaaki Imaizumi
Unbalanced optimal transport (UOT) extends classical optimal transport to measures with different total masses, but statistical guarantees for Monge-type estimation remain limited.…
On gradient descent-ascent flows in metric spaces
Noboru Isobe, Sho Shimoyama
Gradient descent-ascent (GDA) flows play a central role in finding saddle points of bivariate functionals, with applications in optimization, game theory, and robust control. While…
Sinkhorn Algorithm for Sequentially Composed Optimal Transports
Kazuki Watanabe, Noboru Isobe
Sinkhorn algorithm is the de-facto standard approximation algorithm for optimal transport, which has been applied to a variety of applications, including image processing and natur…
Last Iterate Convergence in Monotone Mean Field Games
Noboru Isobe, Kenshi Abe, Kaito Ariu
In the Lasry--Lions framework, Mean-Field Games (MFGs) model interactions among an infinite number of agents. However, existing algorithms either require strict monotonicity or onl…
String Diagram of Optimal Transports
Kazuki Watanabe, Noboru Isobe
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchica…