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Optimal and Practical Algorithms for Smooth and Strongly Convex Decentralized Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply Chebyshev acceleration to APAPC | APAPC · Smooth strongly convex decentralized optimization | gradient computation complexity: \mathcal{O}\left((\sqrt{\kappa \chi} + \chi)\log(1/\varepsilon)\right) -> \mathcal{O}\left(\sqrt{\kappa}\log(1/\varepsil | Helped |
| Apply Chebyshev acceleration to APAPC | APAPC · Smooth strongly convex decentralized optimization | communication complexity: \mathcal{O}\left((\sqrt{\kappa \chi} + \chi)\log(1/\varepsilon)\right) -> \mathcal{O}\left(\sqrt{\kappa\chi}\log(1/\vare | Helped |
| Use accelerated APAPC rather than the PAPC baseline | PAPC · Smooth strongly convex decentralized optimization | condition-number dependence of complexity: \mathcal{O}\left((\kappa+\chi(\mathbf{W}))\log(1/\varepsilon)\right) -> \mathcal{O}\left((\sqrt{\kappa \chi(\mathbf{W})} | Helped |
| Use OPAPC instead of Accelerated Dual Ascent | Decentralized optimization · Smooth strongly convex decentralized optimization | gradient computation complexity: \mathcal{O}\left(\kappa \sqrt{\chi} \log^2\frac{1}{\varepsilon}\right) -> \mathcal{O}\left(\sqrt{\kappa}\log\frac{1}{\va | Helped |
| Avoid dual-gradient computations by using OPAPC | Decentralized optimization · LIBSVM and synthetic logistic-regression experiments | communication rounds | No clear effect |
| Use OPAPC rather than MSDA | Decentralized optimization · LIBSVM and synthetic logistic-regression experiments | gradient computation complexity | Mixed |
| Use OPAPC rather than Accelerated Penalty | Decentralized optimization · LIBSVM and synthetic logistic-regression experiments | gradient computation complexity | No clear effect |
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