Timeline for Iterated optimal transport
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4 at 16:40 | comment | added | leo monsaingeon | another relevant keyword is "multimarginal optimal transport" | |
| Dec 4 at 16:22 | comment | added | leo monsaingeon | Any reasonable answer to this problem should involve the marginals too, since your "second" problem does not depend on $\mu_Y$. For the classical transportation problem where $X=Y=Z$ and $c_1(x,y)=(1-\lambda)|x-y|^2,c_2(y,z)=\lambda |y-z|^2$ and $c_3(x,z)=|x-z|^2$ then your greedy strategry is optimal if and only if $\mu_Y$ is the time-$\lambda$ geodesic interpolation between $\mu_X$ and $\mu_Z$, i-e the pushforward of the optimal plan $\pi_3(x,z)$ under the map $y=T_\lambda(x,z)=(1-\lambda)x+\lambda z$. A keyword here is perhaps McCann's interpolant. | |
| Oct 11 at 15:47 | comment | added | tex.support | Ah yes, sorry for the delay. So I agree with what you have written, and was fully anticipating something like this. What I am interested in is: can one describe how the relationship between $c_1$ and $c_2$ affects the inefficiency of the composed plan. In other words, can one bound the amount you overpay in $c_3$ in terms of how $c_1$ and $c_2$ fit together? In this sense, it is something of an inverse optimal transport question. | |
| Oct 9 at 16:37 | answer | added | Iosif Pinelis | timeline score: 2 | |
| S Oct 9 at 14:58 | review | First questions | |||
| Oct 9 at 17:34 | |||||
| S Oct 9 at 14:58 | history | asked | tex.support | CC BY-SA 4.0 |