---
_id: '14703'
abstract:
- lang: eng
text: We present a discretization of the dynamic optimal transport problem for which
we can obtain the convergence rate for the value of the transport cost to its
continuous value when the temporal and spatial stepsize vanish. This convergence
result does not require any regularity assumption on the measures, though experiments
suggest that the rate is not sharp. Via an analysis of the duality gap we also
obtain the convergence rates for the gradient of the optimal potentials and the
velocity field under mild regularity assumptions. To obtain such rates we discretize
the dual formulation of the dynamic optimal transport problem and use the mature
literature related to the error due to discretizing the Hamilton-Jacobi equation.
acknowledgement: "The authors would like to thank Chris Wojtan for his continuous
support and several interesting discussions. Part of this research was performed
during two visits: one of SI to the BIDSA research center at Bocconi University,
and one of HL to the Institute of Science and Technology Austria. Both host institutions
are warmly acknowledged for the hospital-\r\nity. HL is partially supported by the
MUR-Prin 2022-202244A7YL “Gradient Flows and Non-Smooth Geometric Structures with
Applications to Optimization and Machine Learning”, funded by the European Union
- Next Generation EU. SI is supported in part by ERC Consolidator Grant 101045083
“CoDiNA” funded by the European Research Council."
article_number: '2312.12213'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
- first_name: Hugo
full_name: Lavenant, Hugo
last_name: Lavenant
citation:
ama: Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic
optimal transport using the dual formulation. arXiv. doi:10.48550/arXiv.2312.12213
apa: Ishida, S., & Lavenant, H. (n.d.). Quantitative convergence of a discretization
of dynamic optimal transport using the dual formulation. arXiv. https://doi.org/10.48550/arXiv.2312.12213
chicago: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2312.12213.
ieee: S. Ishida and H. Lavenant, “Quantitative convergence of a discretization of
dynamic optimal transport using the dual formulation,” arXiv. .
ista: Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic
optimal transport using the dual formulation. arXiv, 2312.12213.
mla: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” ArXiv, 2312.12213,
doi:10.48550/arXiv.2312.12213.
short: S. Ishida, H. Lavenant, ArXiv (n.d.).
date_created: 2023-12-21T10:14:37Z
date_published: 2023-12-19T00:00:00Z
date_updated: 2023-12-27T13:44:33Z
day: '19'
department:
- _id: GradSch
- _id: ChWo
doi: 10.48550/arXiv.2312.12213
external_id:
arxiv:
- '2312.12213'
keyword:
- Optimal transport
- Hamilton-Jacobi equation
- convex optimization
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2312.12213
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: arXiv
publication_status: submitted
status: public
title: Quantitative convergence of a discretization of dynamic optimal transport using
the dual formulation
type: preprint
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '10553'
abstract:
- lang: eng
text: The popularity of permissioned blockchain systems demands BFT SMR protocols
that are efficient under good network conditions (synchrony) and robust under
bad network conditions (asynchrony). The state-of-the-art partially synchronous
BFT SMR protocols provide optimal linear communication cost per decision under
synchrony and good leaders, but lose liveness under asynchrony. On the other hand,
the state-of-the-art asynchronous BFT SMR protocols are live even under asynchrony,
but always pay quadratic cost even under synchrony. In this paper, we propose
a BFT SMR protocol that achieves the best of both worlds -- optimal linear cost
per decision under good networks and leaders, optimal quadratic cost per decision
under bad networks, and remains always live.
article_processing_charge: No
arxiv: 1
author:
- first_name: Rati
full_name: Gelashvili, Rati
last_name: Gelashvili
- first_name: Eleftherios
full_name: Kokoris Kogias, Eleftherios
id: f5983044-d7ef-11ea-ac6d-fd1430a26d30
last_name: Kokoris Kogias
- first_name: Alexander
full_name: Spiegelman, Alexander
last_name: Spiegelman
- first_name: Zhuolun
full_name: Xiang, Zhuolun
last_name: Xiang
citation:
ama: 'Gelashvili R, Kokoris Kogias E, Spiegelman A, Xiang Z. Brief announcement:
Be prepared when network goes bad: An asynchronous view-change protocol. In: Proceedings
of the 2021 ACM Symposium on Principles of Distributed Computing. Association
for Computing Machinery; 2021:187-190. doi:10.1145/3465084.3467941'
apa: 'Gelashvili, R., Kokoris Kogias, E., Spiegelman, A., & Xiang, Z. (2021).
Brief announcement: Be prepared when network goes bad: An asynchronous view-change
protocol. In Proceedings of the 2021 ACM Symposium on Principles of Distributed
Computing (pp. 187–190). Virtual, Italy: Association for Computing Machinery.
https://doi.org/10.1145/3465084.3467941'
chicago: 'Gelashvili, Rati, Eleftherios Kokoris Kogias, Alexander Spiegelman, and
Zhuolun Xiang. “Brief Announcement: Be Prepared When Network Goes Bad: An Asynchronous
View-Change Protocol.” In Proceedings of the 2021 ACM Symposium on Principles
of Distributed Computing, 187–90. Association for Computing Machinery, 2021.
https://doi.org/10.1145/3465084.3467941.'
ieee: 'R. Gelashvili, E. Kokoris Kogias, A. Spiegelman, and Z. Xiang, “Brief announcement:
Be prepared when network goes bad: An asynchronous view-change protocol,” in Proceedings
of the 2021 ACM Symposium on Principles of Distributed Computing, Virtual,
Italy, 2021, pp. 187–190.'
ista: 'Gelashvili R, Kokoris Kogias E, Spiegelman A, Xiang Z. 2021. Brief announcement:
Be prepared when network goes bad: An asynchronous view-change protocol. Proceedings
of the 2021 ACM Symposium on Principles of Distributed Computing. PODC: Principles
of Distributed Computing, 187–190.'
mla: 'Gelashvili, Rati, et al. “Brief Announcement: Be Prepared When Network Goes
Bad: An Asynchronous View-Change Protocol.” Proceedings of the 2021 ACM Symposium
on Principles of Distributed Computing, Association for Computing Machinery,
2021, pp. 187–90, doi:10.1145/3465084.3467941.'
short: R. Gelashvili, E. Kokoris Kogias, A. Spiegelman, Z. Xiang, in:, Proceedings
of the 2021 ACM Symposium on Principles of Distributed Computing, Association
for Computing Machinery, 2021, pp. 187–190.
conference:
end_date: 2021-07-30
location: Virtual, Italy
name: 'PODC: Principles of Distributed Computing'
start_date: 2021-07-26
date_created: 2021-12-16T13:20:19Z
date_published: 2021-07-21T00:00:00Z
date_updated: 2023-09-04T11:42:10Z
day: '21'
department:
- _id: ElKo
doi: 10.1145/3465084.3467941
external_id:
arxiv:
- '2103.03181'
isi:
- '000744439800018'
isi: 1
keyword:
- optimal
- state machine replication
- fallback
- asynchrony
- byzantine faults
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.03181
month: '07'
oa: 1
oa_version: Preprint
page: 187-190
publication: Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing
publication_identifier:
isbn:
- 9-781-4503-8548-0
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Brief announcement: Be prepared when network goes bad: An asynchronous view-change
protocol'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...