Research map / Optimization / Nonconvex and smooth optimization
Analytical Study of Momentum-Based Acceleration Methods in Paradigmatic High-Dimensional Non-Convex Problems
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Nesterov acceleration instead of gradient descent | Optimization in the mixed p-spin and spiked matrix-tensor models · Mixed p-spin model | dynamics speed | Helped |
| Use heavy-ball momentum instead of gradient descent | Optimization in the mixed p-spin and spiked matrix-tensor models · Mixed p-spin model | dynamics speed | Helped |
| Use Nesterov acceleration instead of gradient descent | Spiked matrix-tensor recovery · Spiked matrix-tensor model | algorithmic recovery threshold | No clear effect |
| Use heavy-ball momentum instead of gradient descent | Spiked matrix-tensor recovery · Spiked matrix-tensor model | algorithmic recovery threshold | No clear effect |
| Set heavy-ball momentum to β=0.9 rather than the other tested β values (ablation) | Heavy-ball momentum · Mixed p-spin model | speedup | Helped |
| Apply dynamical mean field theory to predict average algorithm dynamics | Nesterov acceleration, heavy-ball momentum, and gradient descent · Mixed p-spin model | agreement with simulations | Helped |
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