optimal transportentropy regularizationKullback-LeiblerBregman projectionconvex optimizationWasserstein barycentergeodesic distancelow-rank approximationsThe optimal transportation theory was successfully applied to different tasks on geometric domains as images and triangle meshes. In these applications the transport ...
00 国际基础科学大会-Critical phenomena from perspective of fuzzy sphere regularization 45:25 国际基础科学大会-From the Sachdev-Ye-Kitaev model to a universal theory of strange 1:09:30 国际基础科学大会-Dynamical degrees-Serge Cantat 52:21 国际基础科学大会-Measure Rigidity beyond Homogeneous Dynamics-...
In the limit ε→ 0 of vanishing regularization, strong compactness holds in L 1 and cluster points are Kantorovich potentials. In particular, the Schrdinger potentials converge in L 1 to the Kantorovich potentials as soon as the latter are unique. These results are proved for al...
On the entropic regularization method for solving min-max problems with applications Consider a min-max problem in the form of min x ε X max 1≤ i ≤ m { f i ( x )}. It is well-known that the non-differentiability of the max function... XS Li,SC Fang - 《Mathematical Methods ...
In the limit $\\varepsilono0$ of vanishing regularization, strong compactness holds in $L^{1}$ and cluster points are Kantorovich potentials. In particular, the Schr\"odinger potentials converge in $L^{1}$ to the Kantorovich potentials as soon as the latter are unique. These results are ...
Optimal transporttensor fieldPSD matricesquantum entropyThis article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This "quantum" formulation of optimal transport (Q-OT) corresponds to a relaxed ...
This entropic regularization allows one to trade the initial Wasserstein fidelity term for a Kulback-Leibler divergence, which is easier to deal with numerically. We show how KL proximal schemes, and in particular Dykstra's algorithm, can be used to compute each step of the regularized flow. ...
Moreover, when solving the capacity constrained multi-marginal optimal transport (CMOT) problem (a special case of our LP problem), our iEPPA is able to bypass the underlying numerical instability issues that often appear in the popular entropic regularization approach, since our algorithm does not...
We consider a class of games with continuum of players where equilibria can\nbe obtained by the minimization of a certain functional related to optimal\ntransport as emphasized in [7]. We then use the powerful entropic\nregularization technique to approximate the problem and solve it numerically ...
optimal transportentropic regularizationSinkhorn divergenceWasserstein distanceThis paper is devoted to the stochastic approximation of entropically regularized-Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal ...