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Federated Minimax Optimization: Improved Convergence Analyses and Algorithms
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the improved Local SGDA analysis | Local SGDA on NC-SC · NC-SC | stochastic gradient complexity: $\mathcal O ( \kappa^{12}/(n \epsilon^6) )$ -> $\mathcal O ( \kappa^4/(n \epsilon^{4}) )$ | Helped |
| Use the improved Local SGDA analysis | Local SGDA on NC-SC · NC-SC | communication rounds: $\mathcal O ( \kappa^8/(n^{1/3} \epsilon^4) )$ -> $\mathcal O ( \kappa^3/\epsilon^{3} )$ | Helped |
| Use the improved Local SGDA analysis | Local SGDA on NC-PL · NC-PL | stochastic gradient complexity: $\mathcal O \left( \max \left\{ \frac{\kappa^3}{n \epsilon^6}, \frac{\kappa^6}{n^2 \epsilon^6} \right\} \right)$ -> $\ma | Helped |
| Use the improved Local SGDA analysis | Local SGDA on NC-PL · NC-PL | communication rounds: $\mathcal O \left( \max \left\{ \frac{\kappa^2}{\epsilon^4}, \frac{\kappa^4}{n^{2/3} \epsilon^4} \right\} \right)$ -> $\ | Helped |
| Use improved Local SGDA+ analysis | Local SGDA+ on NC-C · NC-C | stochastic gradient complexity: $\mathcal O ( \epsilon^{-16} )$ -> $\mathcal O (1/(n \epsilon^{8}))$ | Helped |
| Use improved Local SGDA+ analysis | Local SGDA+ on NC-C · NC-C | communication rounds: $\mathcal O (\epsilon^{-12})$ -> $\mathcal O (1/\epsilon^{7})$ | Helped |
| Use improved Local SGDA+ analysis | Local SGDA+ on NC-1PC · NC-1PC | stochastic gradient complexity: $\mathcal O ( 1/\epsilon^{12} )$ -> $\mathcal O ( 1/\epsilon^{8} )$ | Helped |
| Use improved Local SGDA+ analysis | Local SGDA+ on NC-1PC · NC-1PC | communication rounds: $\mathcal O \left( \frac{n^{1/6}}{\epsilon^{8}} \right)$ -> $\mathcal O ( 1/\epsilon^{7} )$ | Helped |
| Add momentum-based gradient estimators and historic gradient averaging | Local SGDA on NC-PL · FashionMNIST fair classification | worst-distribution test accuracy | Helped |
| Add momentum-based gradient estimators and historic gradient averaging | Local SGDA+ on robust training · CIFAR10 robust neural network training | robust test accuracy | Helped |
| Increase synchronization interval to use more local updates | Local SGDA and Momentum Local SGDA · FashionMNIST fair classification | communication rounds to reach 50% test accuracy | Helped |
| Increase synchronization interval to use more local updates | Local SGDA+ and Momentum Local SGDA+ · CIFAR10 robust neural network training | communication rounds to reach the same accuracy | Helped |
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