Research map / Optimization / Nonconvex and smooth optimization
On the Local Minima of the Empirical Risk
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply Gaussian smoothing and perturbed stochastic gradient descent to the observed function | Pointwise-close approximation f of a smooth nonconvex objective F · Nonconvex objective with polynomially many function queries | function-error tolerance: O(ε^2/d^8) -> O(√(ε^3/ρ)·(1/d)) | Helped |
| Allow exponentially many function queries | Finding an ε-SOSP of F from values of f · Nonconvex objective with unlimited queries | function-error tolerance: ν ≤ O(√(ε^3/ρ)·(1/d)) -> ν ≤ O(√(ε^3/ρ)) | Helped |
| Use a sample size n ≥ Õ(d^4/ε^3) | ZPSGD for learning a ReLU unit · ReLU unit learning | estimation error: ‖ŵ - w*‖ ≤ ε | Helped |
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