1. What contributions have the authors mentioned in the paper "A user’s guide to optimal transport" ?
This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro.
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A User’s Guide to Optimal Transport
Luigi Ambrosio,Nicola Gigli +1 more
- 01 Jan 2013
- pp 1-155
TL;DR: In this paper, the authors provide a quick and reasonably account of the classical theory of optimal mass transportation and its more recent developments, including the metric theory of gradient flows, geometric and functional inequalities related to optimal transportation, the first and second order differential calculus in the Wasserstein space and the synthetic theory of metric measure spaces with Ricci curvature bounded from below.
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Abstract: This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro. It provides a quick and reasonably account of the classical theory of optimal mass transportation and of its more recent developments, including the metric theory of gradient flows, geometric and functional inequalities related to optimal transportation, the first and second order differential calculus in the Wasserstein space and the synthetic theory of metric measure spaces with Ricci curvature bounded from below.
read more
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Distribution functions, extremal limits and optimal transport
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Optimal Transport Based Seismic Inversion: Beyond Cycle Skipping
Björn Engquist,Yunan Yang +1 more
TL;DR: A sharper theorem regarding the convexity of the Wasserstein metric as the objective function is given and it is demonstrated that FWI using optimal transport can recover geophysical properties from domains where no seismic waves travel through.
Complete duality for martingale optimal transport on the line
TL;DR: A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward (cost) functions: absence of a duality gap and existence of dual optimizers.
Wasserstein Flow Meets Replicator Dynamics: A Mean-Field Analysis of Representation Learning in Actor-Critic.
Yufeng Zhang,Siyu Chen,Zhuoran Yang,Michael I. Jordan,Zhaoran Wang +4 more
TL;DR: This work analyzes actor-critic algorithms with overparameterized neural networks, proving global optimality and sublinear convergence in a mean-field, continuous-time, and infinite-width limiting regime with separated timescales.
References
•Book
Optimal Transport: Old and New
Cédric Villani
- 02 Jan 2013
TL;DR: In this paper, the authors provide a detailed description of the basic properties of optimal transport, including cyclical monotonicity and Kantorovich duality, and three examples of coupling techniques.
7.4K
•Book
Topics in Optimal Transportation
Cédric Villani
- 01 Mar 2003
TL;DR: In this paper, the metric side of optimal transportation is considered from a differential point of view on optimal transportation, and the Kantorovich duality of the optimal transportation problem is investigated.
6.1K
•Book
Gradient Flows: In Metric Spaces and in the Space of Probability Measures
Luigi Ambrosio,Nicola Gigli,Giuseppe Savaré +2 more
- 01 Jan 2005
TL;DR: In this article, Gradient flows and curves of Maximal slopes of the Wasserstein distance along geodesics are used to measure the optimal transportation problem in the space of probability measures.
4.1K
•Book
A Course in Metric Geometry
Dmitri Burago,Yuri Burago,Sergei Ivanov +2 more
- 01 Jul 2001
TL;DR: In this article, a large-scale Geometry Spaces of Curvature Bounded Above Spaces of Bounded Curvatures Bounded Below Bibliography Index is presented. But it is based on the Riemannian metric space.