Research map / Optimization / Nonconvex and smooth optimization
On Solving Minimax Optimization Locally: A Follow-the-Ridge Approach
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the Follow-the-Ridge correction to gradient descent-ascent | Minimax optimization on g1 · Toy problem g1 | convergence to local minimax | Helped |
| Add the Follow-the-Ridge correction to gradient descent-ascent | Minimax optimization on g2 · Toy problem g2 | avoidance of non-local-minimax stationary point | Helped |
| Add the Follow-the-Ridge correction to gradient descent-ascent | Minimax optimization on g3 · Toy problem g3 | convergence to local minimax | Helped |
| Use Follow-the-Ridge instead of GDA | GAN training with saturating loss · Mixture of Gaussians | mode coverage | Helped |
| Use Follow-the-Ridge instead of EG | GAN training with saturating loss · Mixture of Gaussians | mode coverage | Helped |
| Use Follow-the-Ridge instead of consensus optimization | GAN training with saturating loss · Mixture of Gaussians | convergence | Helped |
| Use Follow-the-Ridge instead of GDA | GAN training · 2-D mixture of Gaussians | gradient norm | Helped |
| Use Follow-the-Ridge instead of GDA | GAN training · MNIST classes 0 and 1 | gradient norm convergence | Helped |
| Use Follow-the-Ridge instead of GDA | GAN training · GAN parameter path | rotational behavior | Helped |
| Use positive momentum with Follow-the-Ridge | Follow-the-Ridge · Local minimax optimization | asymptotic convergence rate: Omega(kappa^{-2}) -> Omega(kappa^{-1}) | Helped |
| Use positive-definite preconditioning with Follow-the-Ridge | Follow-the-Ridge · Local minimax optimization | local convergence guarantees | No clear effect |
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