Research map / Optimization / Implicit bias and generalization
Algorithmic Stability of Heavy-Tailed SGD with General Loss Functions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a dissipativity-based pseudo-Lipschitz stability analysis of heavy-tailed SDEs to derive Wasserstein stability bounds for general (possibly non-convex) losses instead of only quadratic losses | heavy-tailed SGD SDE (alpha-stable Levy-driven) · theoretical generalization bound | generalization bound order | No clear effect |
| Increase tail heaviness (smaller alpha) in the stability bound constant g(alpha;d) for large dimension d | Wasserstein stability bound / generalization bound · theoretical analysis, dimension d >= d_0 | bound behavior in alpha | Mixed |
| Euler-Maruyama discretization with sufficiently small step-size applied to the heavy-tailed SDE | discrete-time heavy-tailed SGD proxy · theoretical stability bound | W1 discretization error order | No clear effect |
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