Buongiorno a tutti,

 

Vorremmo segnalarvi che il seminario di domani (in basso titolo e abstract) sarà trasmesso anche in streaming, al seguente link zoom:

 

Argomento: Zoom meeting invitation - Riunione Zoom di Alekos Cecchin

Ora: 29 nov 2024 02:30 PM Roma

 

Entra Zoom Riunione

https://unipd.zoom.us/j/81514054943?pwd=TnXbQeiqRjhZVHdHsUeu3QMAEaRwIB.1

 

ID riunione: 815 1405 4943

Codice d’accesso: 358217

 

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Da: alekos.cecchin@unipd.it <alekos.cecchin@unipd.it>
Inviato: venerdì 22 novembre 2024 21:00
A: random@mail.dm.unipi.it
Oggetto: Seminario Padova - Alex Delalande

 

Buongiorno a tutti,

 

Vorremmo segnalarvi che venerdì prossimo (29 Novembre) alle ore 14:30 in aula 2BC30 (Torre Archimede, Università di Padova) ci sarà un seminario per il ciclo di seminari in Probabilità e Finanza di:

 

Alex Delalande (EPFL Losanna)
https://alex-delalande.github.io

 
Title: Sharper Exponential Convergence Rates for Sinkhorn's Algorithm in Continuous Settings


Date: November 29, 2024, at 14:30, room 2BC30


Abstract: In this talk, I will present recent results I obtained in collaboration with Lénaïc Chizat and Tomas Vaškevičius regarding the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems, in the context where at least one of the probability measures, say \mu, admits a density over \R^d. For a semi-concave cost function bounded by c∞ and a regularization parameter 
λ>0, we obtained exponential convergence guarantees on the dual sub-optimality gap with contraction rates that are polynomial in λ/c∞. This represents an exponential improvement over the known contraction rate 1−Θ(exp(−c∞/λ)) achievable via Hilbert's projective metric. Specifically, we proved a contraction rate value of 1−Θ(λ²/c²∞) when  has a bounded log-density. In some cases, such as when  is log-concave and the cost function is c(x,y)=−x,y, this rate improves to 1−Θ(λ/c∞). The latter rate matches the one that we derived for the transport between isotropic Gaussian measures, indicating tightness in the dependency in λ/c∞. Our results are fully non-asymptotic and explicit in all the parameters of the problem.

 

Vi aspettiamo numerosi!

 

Alberto Chiarini e Alekos Cecchin

 

Sito web del seminario: https://www.math.unipd.it/~chiarini/seminars/