Establishes L^∞-stability of dual potentials in QOT, yielding local Lipschitz stability of the optimal coupling support in Hausdorff distance for quadratic cost under marginal perturbations.
Gluing methods for quantitative stability of optimal transport maps
6 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 6representative citing papers
Lipschitz L² stability estimates for OT maps in terms of 2-MK distance (and C^{1,α} under Hölder) plus explicit second variation of quadratic MK distance via Monge-Ampère linearization.
A new estimator for Monge transport maps is proposed based on Brenier potentials with convergence rates in semi-discrete settings.
A new constrained gradient flow on the space of transport maps converges to the OT map and enables more stable and accurate training of convexity-constrained neural networks for learning Monge maps.
Proves graphical convergence of empirical subdifferentials for sampled OT objectives to the population subdifferential, ensuring subgradient methods approach stationary points of the true problem.
The paper characterizes stability of the Kim-Milman flow map with respect to target measure variations measured in relative Fisher information.
citing papers explorer
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Stability of Quadratically Regularized Optimal Transport
Establishes L^∞-stability of dual potentials in QOT, yielding local Lipschitz stability of the optimal coupling support in Hausdorff distance for quadratic cost under marginal perturbations.
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Stability of optimal transport maps and second variation of the 2-Monge-Kantorovich distance
Lipschitz L² stability estimates for OT maps in terms of 2-MK distance (and C^{1,α} under Hölder) plus explicit second variation of quadratic MK distance via Monge-Ampère linearization.
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Statistical Estimation of Monge Transport Maps via Brenier Potentials
A new estimator for Monge transport maps is proposed based on Brenier potentials with convergence rates in semi-discrete settings.
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Learning Monge maps with constrained drifting models
A new constrained gradient flow on the space of transport maps converges to the OT map and enables more stable and accurate training of convexity-constrained neural networks for learning Monge maps.
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Convergence of empirical subgradients for optimal transport-based objectives
Proves graphical convergence of empirical subdifferentials for sampled OT objectives to the population subdifferential, ensuring subgradient methods approach stationary points of the true problem.
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Stability of the Kim--Milman flow map
The paper characterizes stability of the Kim-Milman flow map with respect to target measure variations measured in relative Fisher information.