Research map / Optimization / Nonconvex and smooth optimization
Provable Acceleration of Heavy Ball beyond Quadratics for a Class of Polyak-Lojasiewicz Functions when the Non-Convexity is Averaged-Out
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Heavy Ball momentum rather than gradient descent | PL optimization with an averaged-out positive-definite average Hessian · PL functions with averaged-out non-convexity | instantaneous convergence rate after burn-in: 1 - Θ(1/κ_t) -> 1 - Θ(1/√κ_t) | Helped |
| Set momentum adaptively using the current minimum eigenvalue of the average Hessian | Heavy Ball · PL functions with averaged-out non-convexity | instantaneous convergence rate: 1 - Θ(1/√κ) -> 1 - Θ(1/√κ_t) | Helped |
| Use constant momentum instead of adaptive momentum (ablation) | Heavy Ball · PL functions with averaged-out non-convexity | instantaneous convergence rate: 1 - Θ(1/√κ_t) -> 1 - Θ(1/√κ) | Hurt |
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