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A Sufficient Condition for Convergences of Adam and RMSProp
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Set the second-moment parameter schedule to θ_t = 1 − (0.01 + 0.99r)/t^r with r = 1.0, 0.75, or 0.5 (ablation) | Generic Adam · Synthetic counterexample | convergence | Helped |
| Set the second-moment parameter schedule to θ_t = 1 − (0.01 + 0.99r)/t^r with r = 0 or 0.25 (ablation) | Generic Adam · Synthetic counterexample | convergence | Hurt |
| Use θ_t = 1 − 0.01/t^r with r = 0.25 instead of the schedule with numerator 0.01 + 0.99r (ablation) | Generic Adam · Synthetic counterexample | convergence | Helped |
| Increase r along the tested second-moment schedules (ablation) | Generic Adam · Synthetic counterexample | convergence speed | Helped |
| Vary the second-moment parameter schedule across r ∈ {0, 0.25, 0.5, 0.75, 1} (ablation) | Generic Adam · LeNet on MNIST | test accuracy | Mixed |
| Vary the second-moment parameter schedule across r ∈ {0, 0.25, 0.5, 0.75, 1} (ablation) | Generic Adam · ResNet-18 on CIFAR-100 | test accuracy | Mixed |
| Use constant θ instead of an increasing θ_t schedule (ablation) | Generic Adam · LeNet on MNIST | training loss | Hurt |
| Use constant θ instead of an increasing θ_t schedule (ablation) | Generic Adam · ResNet-18 on CIFAR-100 | test accuracy | Hurt |
| Use constant θ instead of an increasing θ_t schedule (ablation) | Generic Adam · ResNet-18 on CIFAR-100 | training loss | Hurt |
| Use a larger r in the second-moment parameter schedule (ablation) | Generic Adam · LeNet on MNIST | convergence speed | Helped |
| Use a larger r in the second-moment parameter schedule (ablation) | Generic Adam · ResNet-18 on CIFAR-100 | convergence speed | Helped |
| Use a polynomially increasing weight sequence w_t = t^r with EMA momentum (ablation) | Weighted AdaEMA · Non-convex stochastic optimization | convergence rate: O(log(T)/√T) | Helped |
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