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Extremal Domain Translation with Neural Optimal Transport
P. 40381–40413.
Gazdieva M., Alexander Korotin, Daniil Selikhanovych, Evgeny Burnaev
In book
Curran Associates, Inc., 2023.
Kolesnikov A., Popova S., Математические заметки 2026 Т. 119 № 3 С. 377–390
We consider the problem of optimal exchange which can be formulated as a kind of optimal transportation problem. The existence of an optimal solution and a duality theorem for the optimal exchange problem are proved in case of completely regular topological spaces. We show the connection between the problem of optimal exchange and the optimal ...
Added: March 12, 2026
Gladin E., Dvurechensky P., Mielke A. et al., , in: 38th Conference on Neural Information Processing Systems (NeurIPS 2024).: [б.и.], 2024. P. 14484–14508.
Added: November 28, 2024
Dvinskikh D., Optimization Methods and Software 2022 Vol. 37 No. 5 P. 1603–1635
In the machine learning and optimization community, there are two main approaches for the convex risk minimization problem, namely the Stochastic Approximation (SA) and the Sample Average Approximation (SAA). In terms of the oracle complexity (required number of stochastic gradient evaluations), both approaches are considered equivalent on average (up to a logarithmic factor). The total complexity depends on ...
Added: March 27, 2024
Asadulaev A., Korotin A., Vage Egiazarian et al., , in: Proceedings of the 12th International Conference on Learning Representations (ICLR 2024).: ICLR, 2024.
Added: March 5, 2024
Tupitsa, N., Dvurechensky P., Gasnikov A. et al., , in: 2020 IEEE 59th Conference on Decision and Control (CDC).: IEEE, 2020. P. 6132–6137.
We study multimarginal optimal transport (MOT) problems, which include, as a particular case, the Wasserstein barycenter problem. In MOT problems, one has to find an optimal coupling between m probability measures, which amounts to finding a tensor of order m. We propose a method based on accelerated alternating minimization and estimate the complexity to find ...
Added: February 5, 2021
Kroshnin A., Spokoiny V., Suvorikova A., Annals of Applied Probability 2021 Vol. 31 No. 3 P. 1264–1298
n this work we introduce the concept of Bures-Wasserstein barycenter $Q_*$, that is essentially a Fr\'echet mean of some distribution $P$ supported on a subspace of positive semi-definite Hermitian operators $\mathbb{H}_{+}(d)$.
We allow a barycenter to be constrained to some affine subspace of $\mathbb{H}_{+}(d)$ and provide conditions ensuring its existence and uniqueness.
We also investigate convergence and concentration properties ...
Added: October 30, 2020
Tupitsa N., Gasnikov A., Dvurechensky P. et al., , in: Mathematical Optimization Theory and Operations Research. MOTOR 2020. Communications in Computer and Information ScienceVol. 1275.: Springer, 2020. P. 192–204.
In this paper we experimentally check a hypothesis, that dual problem to discrete entropy regularized optimal transport problem possesses strong convexity on a certain compact set. We present a numerical estimation technique of parameter of strong convexity and show that such an estimate increases the performance of an accelerated alternating minimization algorithm for strongly convex ...
Added: October 28, 2020
Kroshnin A., Tupitsa Nazarii, Dvinskikh D. et al., , in: Proceedings of Machine Learning ResearchVol. 97: International Conference on Machine Learning, 9-15 June 2019, Long Beach, California, USA.: PMLR, 2019. P. 3530–3540.
We study the complexity of approximating the Wasserstein barycenter of m discrete measures, or histograms of size n, by contrasting two alternative approaches that use entropic regularization. The first approach is based on the Iterative Bregman Projections (IBP) algorithm for which our novel analysis gives a complexity bound proportional to $m n^2 / \epsilon^2$ to approximate the original non-regularized barycenter. ...
Added: June 11, 2019
Kroshnin A., Journal of Convex Analysis 2018 Vol. 25 No. 4 P. 1371–1395
We consider the space P(X) of probability measures on arbitrary Radon space X endowed with a transportation cost J(μ, ν) generated by a nonnegative continuous cost function. For a probability distribution on P(X) we formulate a notion of average with respect to this transportation cost, called here the Fréchet barycenter, prove a version of the law ...
Added: November 23, 2018
Kolesnikov A., Tikhonov S. Y., / Series math "arxiv.org". 2012. No. 1203.3457.
Let $\mu = e^{-V} \ dx$ be a probability measure and $T = \nabla \Phi$ be the optimal transportation mapping pushing forward $\mu$ onto a log-concave compactly supported measure $\nu = e^{-W} \ dx$. In this paper, we introduce a new approach to the regularity problem for the corresponding Monge--Amp{\`e}re equation $e^{-V} = \det D^2 ...
Added: March 28, 2013
Delon J., Salomon J., Sobolevski A., SIAM Journal of Discrete Mathematics 2012 Vol. 26 No. 2 P. 801–827
In this paper, we introduce a class of local indicators that enable us to compute efficiently optimal transport plans associated with arbitrary weighted distributions of N demands and M supplies in R in the case where the cost function is concave. Indeed, whereas this problem can be solved linearly when the cost is a convex ...
Added: May 30, 2012