Research map / Optimization / Nonconvex and smooth optimization
On the Curved Geometry of Accelerated Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the dual Bregman geometry of f* to construct the accelerated gradient dynamics from the proximal point method | Proposed AGM ODE · Strongly convex, L-smooth quadratic objectives | continuous-time decay rate: \rho_{\text{AGM}}\geq\frac{1}{2}\sqrt{\frac{\mu}{L}} | Helped |
| Set the inertia parameter α anywhere in [0,1] (ablation) | AGM ODE · Strongly convex, L-smooth quadratic objectives | continuous-time decay rate: ρ=\frac{1}{2}\sqrt{\frac{\mu}{L}} | No clear effect |
| Remove the extra inertia by setting α=0 (ablation) | Proximal-point-derived method · General convex problems | accelerated convergence rate | Hurt |
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