Research map / Optimization / Nonconvex and smooth optimization
Convergence of Gradient Methods on Bilinear Zero-Sum Games
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Gauss–Seidel instead of Jacobi updates for GD | GD · Bilinear zero-sum games | convergence | Mixed |
| Use Gauss–Seidel instead of Jacobi updates for EG | EG · Bilinear zero-sum games | convergence region | Helped |
| Use Gauss–Seidel instead of Jacobi updates for OGD | OGD · Bilinear zero-sum games | convergence region | Helped |
| Use Gauss–Seidel instead of Jacobi updates for momentum | Momentum · Bilinear zero-sum games | convergence | Helped |
| Tune EG parameters to α → 0 and β₁ = β₂ = 2/(σ₁² + σₙ²) (ablation) | Jacobi and Gauss–Seidel EG · Bilinear zero-sum games | optimal linear convergence rate exponent: ∼ 1 - 2/κ^2 | Helped |
| Use Jacobi OGD with α = 2β and tune β to β* (ablation) | Jacobi OGD · Bilinear zero-sum games | optimal linear convergence rate exponent: ∼ 1 - 1/(6κ^2) | Helped |
| Use Gauss–Seidel OGD with β₂ = 0 and tune α and β₁ (ablation) | Gauss–Seidel OGD · Bilinear zero-sum games | optimal linear convergence rate exponent: ∼ 1 - 1/κ^2 | Helped |
| Use Gauss–Seidel momentum with β₁ = -1/2 and β₂ = 0 (ablation) | Gauss–Seidel momentum · Bilinear zero-sum games | optimal linear convergence rate exponent: ∼ 1 - 2/(9κ^2) | Helped |
| Use Jacobi momentum instead of Gauss–Seidel momentum | Momentum · Bilinear zero-sum games | convergence | Hurt |
| Use α = 1/2, β = 1/3 instead of α = 1/2, β = 1/4 (ablation) | OGD · One-dimensional bilinear game, σ = 1 | spectral radius: 0.966 -> 0.956 | Helped |
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