Proves near-Lipschitz stability in 2-Wasserstein distance (up to log factor) and relative entropy stability for the Kim-Milman flow map w.r.t. target measure perturbations under regularity assumptions, with existence for finite second moment targets.
Stability bounds for smooth optimal transport maps and their statistical implications
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Establishes a general lower bound of order ε^{1/(d+2)} on the localization rate of QOT optimizers around the Monge coupling in directed Hausdorff distance, with sharper affine-case tube bounds.
Estimators for transport-growth pairs in unbalanced OT achieve minimax optimal rates, supported by a value-based stability reduction through a UOT gap condition.
The paper characterizes stability of the Kim-Milman flow map with respect to target measure variations measured in relative Fisher information.
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Near-Lipschitz stability of the Kim--Milman flow map
Proves near-Lipschitz stability in 2-Wasserstein distance (up to log factor) and relative entropy stability for the Kim-Milman flow map w.r.t. target measure perturbations under regularity assumptions, with existence for finite second moment targets.
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Quadratically Regularized Optimal Transport: Localization Bounds and Affine Case Analysis
Establishes a general lower bound of order ε^{1/(d+2)} on the localization rate of QOT optimizers around the Monge coupling in directed Hausdorff distance, with sharper affine-case tube bounds.
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Minimax Optimal Estimation of Transport-Growth Pairs in Unbalanced Optimal Transport
Estimators for transport-growth pairs in unbalanced OT achieve minimax optimal rates, supported by a value-based stability reduction through a UOT gap condition.
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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.