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On the Complexity of Approximating Wasserstein Barycenters
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use IBP with a regularization parameter chosen proportional to the target accuracy | Wasserstein barycenter approximation · Non-regularized Wasserstein barycenter | arithmetic operations: \widetilde{O}\left(\frac{c^2mn^2}{\varepsilon^2}\right) | Mixed |
| Use accelerated primal-dual gradient descent instead of IBP | Wasserstein barycenter approximation · Non-regularized Wasserstein barycenter | arithmetic operations: \widetilde{O}(mn^{2.5}/\varepsilon) | Helped |
| Use entropic regularization with accuracy-scaled regularization parameter | IBP and accelerated gradient descent · High-accuracy Wasserstein barycenter approximation | algorithm stability | Hurt |
| Use KL-proximal steps, solving each step with IBP | Wasserstein barycenter approximation · Non-regularized Wasserstein barycenter | dependence on ε in complexity: 1/ε^2 → 1/ε | Helped |
| Use accelerated primal-dual gradient descent with graph-based consensus constraints | Wasserstein barycenter approximation · Arbitrary connected undirected network | distributed scalability | Helped |
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