Research map / Optimization / Nonconvex and smooth optimization
Improved Algorithms for Convex-Concave Minimax Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Proximal Best Response instead of the Lin et al. algorithm | Strongly convex-strongly concave minimax optimization · General smooth strongly convex-strongly concave problems, especially when L_{xy} is much smaller than L | gradient complexity: \tilde{O}\left(\sqrt{\frac{L_\mathbf{x}}{m_\mathbf{x}}+\frac{L\cdot L_{\mathbf{x}\mathbf{y}}}{m_\mathbf{x} m_\mathbf{y}} | Helped |
| Use RHSS(k) with optimized k | Quadratic strongly convex-strongly concave minimax optimization · Quadratic saddle-point problems | matrix-vector products: \sqrt{\frac{L_{\mathbf{x}\mathbf{y}}^2}{m_\mathbf{x} m_\mathbf{y}}+\frac{L_\mathbf{x}}{m_\mathbf{x}}+\frac{L_\mathbf{y}} | Helped |
| Use Alternating Best Response when the interaction is sufficiently weak | Strongly convex-strongly concave minimax optimization · L_{xy} < 1/2 sqrt(m_x m_y) | gradient complexity: O\left(\left(\sqrt{\kappa_\mathbf{x}+\kappa_\mathbf{y}}\right)\cdot \ln\left(\kappa_\mathbf{x}\kappa_\mathbf{y}\right)\l | Helped |
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