Research map / Optimization / Nonconvex and smooth optimization
The Step Decay Schedule: A Near Optimal, Geometrically Decaying Learning Rate Procedure For Least Squares
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace polynomially decaying stepsizes with Step Decay | Final-iterate SGD for strongly convex least squares · Strongly convex least squares, fixed horizon | final-iterate excess risk: \Omega\left( \frac{\sigma^2 d}{T} \cdot \red{\kappa} \right) -> \order{ \frac{\sigma^2 d}{T} \cdot \red{\log T}} | Helped |
| Replace polynomially decaying stepsizes with Step Decay | Final-iterate SGD for non-strongly convex least squares · Non-strongly convex least squares, fixed horizon | final-iterate excess risk: \Omega\left( \frac{\sigma^2 d}{T} \cdot \red{\frac{\sqrt{T}}{\log T}} \right) -> \order{ \frac{\sigma^2 d}{T} \cdot \red | Helped |
| Use exponential decay rather than O(1/t) | preresnet-44 · CIFAR-10, 100 epochs | train function value: 0.0713\pm0.015 -> 0.0053\pm 0.0015 | Helped |
| Use exponential decay rather than O(1/t) | preresnet-44 · CIFAR-10, 100 epochs | test 0/1 error: 10.20\pm0.7\% -> 7.58\pm0.21\% | Helped |
| Use exponential decay rather than O(1/√t) | preresnet-44 · CIFAR-10, 100 epochs | train function value: 0.1119\pm 0.036 -> 0.0053\pm 0.0015 | Helped |
| Use exponential decay rather than O(1/√t) | preresnet-44 · CIFAR-10, 100 epochs | test 0/1 error: 11.6\pm0.67\% -> 7.58\pm0.21\% | Helped |
| Tune exponential-decay hyperparameters for 33 rather than 100 epochs (ablation) | Exponential decay on preresnet-44 · CIFAR-10, evaluated at 100 epochs | test 0/1 error: 7.58\pm0.21\% -> 8.57\pm0.25\% | Hurt |
| Tune exponential-decay hyperparameters for 66 rather than 100 epochs (ablation) | Exponential decay on preresnet-44 · CIFAR-10, evaluated at 100 epochs | test 0/1 error: 7.58\pm0.21\% -> 8.46\pm0.19\% | Hurt |
| Average suffix iterates instead of using the final iterate (ablation) | SGD with polynomial decay on preresnet-44 · CIFAR-10 | generalization behavior | Hurt |
| Average only the final few (≤ 5) epochs rather than using the final iterate (ablation) | SGD on preresnet-44 · CIFAR-10 | generalization behavior | No clear effect |
Closest papers by meaning
- On the Convergence of Step Decay Step-Size for Stochastic Optimization (NeurIPS 2021 · similarity 0.92)
- Fast Last-Iterate Convergence of SGD in the Smooth Interpolation Regime (NeurIPS 2025 · similarity 0.90)
- Revisiting the Last-Iterate Convergence of Stochastic Gradient Methods (ICLR 2024 · similarity 0.89)
- Last-Iterate Convergence of Single-Loop Stochastic Methods for Constrained Convex-Concave Minimax Problems (NeurIPS 2026 · similarity 0.89)
- Controlling the Flow: Stability and Convergence for Stochastic Gradient Descent with Decaying Regularization (NeurIPS 2025 · similarity 0.89)
- Rapid Overfitting of Multi-Pass SGD in Stochastic Convex Optimization (ICML 2025 · similarity 0.89)
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