Research map / Optimization / Nonconvex and smooth optimization
Leveraging Non-uniformity in First-order Non-convex Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Normalize the policy gradient | PG · One-state MDP | suboptimality convergence rate: O(1/t) -> O(e^{- c \cdot t}) | Helped |
| Normalize the policy gradient | PG · Finite MDP | value suboptimality convergence rate: O(1/t) -> O(e^{-c \cdot t}) | Helped |
| Use geometry-aware normalization instead of standard gradient normalization | GLM MSE optimization · GLM MSE | suboptimality convergence rate: O(1/\sqrt{t}) -> O(e^{-c \cdot t}) | Helped |
| Use GNGD rather than GD | GLM MSE optimization · GLM MSE | convergence-rate constant: C^2 -> C | Helped |
| Use GNGD rather than GD | Non-uniformly smooth objectives satisfying case (1) · Objectives with \xi < 1/2 | suboptimality convergence rate: \Theta(1/t^{\frac{1}{1 - 2 \xi}}) -> O(e^{-t}) | Helped |
| Use GNGD rather than GD | Objectives satisfying case (3) · Objectives with \xi \in (1/2, 1) | convergence: GD does not converge -> O(e^{-t}) | Helped |
| Use GNGD rather than GD | GLM MSE optimization · GLM MSE plateaus | plateau escape | Helped |
| Use normalized PG rather than standard PG | Policy optimization · One-state MDP | plateau escape | Helped |
| Use fixed-step NGD instead of geometry-aware normalization | GLM MSE optimization · GLM MSE | convergence-rate guarantee: O(e^{-c \cdot t}) -> O(1/\sqrt{t}) | Hurt |
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