Derives the cold Sinkhorn limiting dynamics as tau approaches zero, proving finite-time convergence to unregularized OT and improved O(tau^{-1}) iteration complexity for dual suboptimality.
Quantitative contraction rates for Sinkhorn's algorithm: beyond bounded costs and compact marginals
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We show non-asymptotic exponential convergence of Sinkhorn iterates to the Schr\"odinger potentials, solutions of the quadratic Entropic Optimal Transport problem on $\mathbb{R}^ d$. Our results hold under mild assumptions on the marginal inputs: in particular, we only assume that they admit an asymptotically positive log-concavity profile, covering as special cases log-concave distributions and bounded smooth perturbations of quadratic potentials. Up to the authors' knowledge, these are the first results which establish exponential convergence of Sinkhorn's algorithm in a general setting without assuming bounded cost functions or compactly supported marginals.
fields
math.OC 3years
2026 3representative citing papers
Proves sharp O(1/k) rate for Sinkhorn via local bipartite graph analysis of positive-mass edges, bootstrapped from prior almost-sharp global bound.
A proof blueprint establishes robust O(1/k) rates for entropic Bregman projections that scale linearly in the inverse regularization strength, instantiated as a new flow-Sinkhorn method for graph W1 with O(p diameter^3 / ε^4) complexity.
citing papers explorer
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Effective dynamics of the Sinkhorn algorithm in the regime of low entropy regularization
Derives the cold Sinkhorn limiting dynamics as tau approaches zero, proving finite-time convergence to unregularized OT and improved O(tau^{-1}) iteration complexity for dual suboptimality.
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Sharp $O(1/k)$ convergence rate for the Sinkhorn algorithm via a local analysis
Proves sharp O(1/k) rate for Sinkhorn via local bipartite graph analysis of positive-mass edges, bootstrapped from prior almost-sharp global bound.
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Robust Sublinear Convergence Rates for Iterative Bregman Projections
A proof blueprint establishes robust O(1/k) rates for entropic Bregman projections that scale linearly in the inverse regularization strength, instantiated as a new flow-Sinkhorn method for graph W1 with O(p diameter^3 / ε^4) complexity.