Timeline for Schrödinger Bridge for other costs
Current License: CC BY-SA 4.0
11 events
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| May 30, 2023 at 6:18 | comment | added | nico | I must admit, I use WFR :) And agree re: Christian's surveys, I am already noticing how much more I learn each time through! Thanks again for the pointer, this was super helpful | |
| May 30, 2023 at 4:36 | comment | added | leo monsaingeon | One should always read the surveys, when they exist ;-) I have to admit that Christian's works are sometimes hard to read the first time, but it's really worth on'es time and investments. And thanks for the compliment (funny that you call it KFR, we were the ones to suggest the name and I kind of liked it but it didn't stick, nowadays it's either WFR or HK!) | |
| May 30, 2023 at 2:36 | comment | added | nico | Actually Léonard 2010 Thm. 4.1 appears to provide the result arxiv.org/pdf/1011.2564.pdf | |
| May 30, 2023 at 2:20 | comment | added | nico | Thanks! also love your work on Kantorovich-Fisher-Rao :) I was aware of the survey, but now notice the relevant parts and see the example $c(v_t) = \|v\|^m$ in arxiv.org/pdf/1011.2564.pdf. Will brush up on LD theory and try for others as well, unless a solution is obvious | |
| May 29, 2023 at 19:46 | comment | added | leo monsaingeon | the link between the entropy minimization and the Benamou-Brenier/optimal-control formulations is then given by Girsanov's theorem | |
| May 29, 2023 at 19:43 | comment | added | leo monsaingeon | I strongly suggest reading Christian Léonard's survey arxiv.org/abs/1308.0215 where the stochastic point of view is detailed. The starting point (also in Schrödinger's original papers!) is an entropy minimization problem over path measures, with respect to a reference measure of your liking. In the case of the reversible Wiener measure you get exactly what you wrote, but one can cover more general situations. The static cost function is the related to the rate functional in a large deviation problem. | |
| May 29, 2023 at 14:39 | history | edited | LSpice | CC BY-SA 4.0 |
Schrodinger -> Schrödinger
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| May 29, 2023 at 14:18 | history | edited | nico | CC BY-SA 4.0 |
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| May 29, 2023 at 6:05 | history | edited | nico | CC BY-SA 4.0 |
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| May 29, 2023 at 3:23 | history | edited | nico | CC BY-SA 4.0 |
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| May 29, 2023 at 3:18 | history | asked | nico | CC BY-SA 4.0 |