Research map / Optimization / Nonconvex and smooth optimization
Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn’s Algorithm
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use APDAGD instead of Sinkhorn’s algorithm | Discrete OT distance approximation · General discrete OT | arithmetic operations: eO\left(\min\left\{\frac{n^{9/4}}{\varepsilon}, \frac{n^2}{\varepsilon^2}\right\}\right) vs. eO\left(\frac{n^2}{\varepsi | Helped |
| Improve the analysis of Sinkhorn’s algorithm | Sinkhorn’s algorithm · General discrete OT | arithmetic operations: O\left(\frac{n^2\|C\|_\infty^3\ln n}{\varepsilon^3}\right) -> O\left(\frac{n^2\|C\|_\infty^2\ln n}{\varepsilon^2}\right) | Helped |
| Use accelerated gradient methods with a line-search strategy and primal-dual updates | APDAGD · Regularized OT with linear constraints | convergence rate: f(ˆxk) − f* ≤ 16∥A∥²E→HR²/(γk²) | Helped |
| Use APDAGD with strongly convex regularizers beyond entropy | APDAGD · Regularized OT | regularizer applicability | Helped |
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