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Generalization Bounds using Lower Tail Exponents in Stochastic Optimizers
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a smaller lower-tail exponent around a local minimum | Stochastic optimizer trajectory · Generalization bound | accumulated generalization gap: C\sqrt{\alpha / n} | Helped |
| Vary the SGD step-size/batch-size ratio | Constant-step SGD · MNIST and CIFAR10; FCN5, FCN7, CNN9 | lower-tail exponent | Mixed |
| Increase the lower-tail exponent | Constant-step SGD · MNIST and CIFAR10; FCN5, FCN7, CNN9 | generalization gap: 10^{-12} to 10^{-4} | Hurt |
| Compare lower-tail and upper-tail exponent estimates | Constant-step SGD · MNIST and CIFAR10; FCN5, FCN7, CNN9 | correlation: 10^{-9} to 10^{-1} | Helped |
| Measure the Fernique–Talagrand functional over recent training iterates | Three-layer fully connected network · Wine Quality UCI | test error correlation | Mixed |
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