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/
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/
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alekos.cecchin＠unipd.it