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Gradient-Free Methods for Deterministic and Stochastic Nonsmooth Nonconvex Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add a post-optimization phase that estimates candidate gradient norms and selects the smallest (ablation) | GFM · Lipschitz nonsmooth nonconvex optimization | function value oracle calls for a high-probability solution: O\left(d^{\frac{3}{2}}\left(\frac{L^4}{\Lambda^4\epsilon^4} + \frac{\Delta L^3}{\delta\Lambda^4\epsilon^4}\right)\right) | Helped |
| Add a post-optimization phase that estimates candidate gradient norms and selects the smallest (ablation) | SGFM · Stochastic Lipschitz nonsmooth nonconvex optimization | noisy function value oracle calls for a high-probability solution: O\left(d^{\frac{3}{2}}\left(\frac{G^4}{\Lambda^4\epsilon^4} + \frac{\Delta G^3}{\delta\Lambda^4\epsilon^4}\right)\right) | Helped |
| Increase the batch size used to estimate candidate gradients (ablation) | 2-SGFM · MNIST image classification | train loss and test loss | Helped |
| Use a more aggressive learning rate rather than the conservative 0.0001 choice (ablation) | 2-SGFM · MNIST image classification | train loss and test loss | Helped |
| Use 2-SGFM instead of gradient-based SGD, Adagrad, or Adam | MNIST image classification · MNIST image classification | training/test accuracy and loss | No clear effect |
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