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First Exit Time Analysis of Stochastic Gradient Descent Under Heavy-Tailed Gradient Noise
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| decrease the discretization step size | Euler-discretized Lévy SDE · Synthetic Ornstein–Uhlenbeck model | first-exit-time error | Helped |
| increase the noise amplitude ε in the small-noise regime | Euler-discretized Lévy SDE · Synthetic Ornstein–Uhlenbeck model | first-exit-time error | Helped |
| increase the noise amplitude ε at larger values | Euler-discretized Lévy SDE · Synthetic Ornstein–Uhlenbeck model | first-exit-time error | Mixed |
| increase the Gaussian noise scale σ | Euler-discretized Lévy SDE · Synthetic Ornstein–Uhlenbeck model | first-exit-time error | Helped |
| increase dimension d | Euler-discretized Lévy SDE · Synthetic Ornstein–Uhlenbeck model | first-exit-time error | Mixed |
| increase dimension from 70 to 100 at α=1.2 | Euler-discretized Lévy SDE · Synthetic Ornstein–Uhlenbeck model | first-exit-time error | Hurt |
| increase network width or depth | SGD on a fully connected ReLU network · MNIST | first-exit-time error | Hurt |
| decrease the step size as network width or depth increases | SGD on a fully connected ReLU network · MNIST | first-exit-time error | Helped |
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