Research map / Optimization / Nonconvex and smooth optimization
Accelerated Algorithms for Smooth Convex-Concave Minimax Problems with O(1/k^2) Rate on Squared Gradient Norm
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Anchoring combined with extragradient steps (EAG) with anchoring coefficient 1/(k+2) | extragradient on smooth convex-concave minimax · smooth convex-concave minimax, squared gradient norm of last iterate | convergence rate of ||G(zk)||^2 | Helped |
| Varying step-size EAG-V vs constant step-size EAG-C | EAG · smooth convex-concave minimax, theoretical constant | constant in rate bound: 27 (EAG-V) vs 260 (EAG-C) | Helped |
| Tuning anchoring exponent delta and alpha0 in EAG-V (ablation) | EAG-V · smooth convex-concave minimax, theoretical constant | constant in rate bound: 27 -> 24.44 | Helped |
| Anchoring added to gradient descent-ascent/extragradient (anchoring removed reverts to plain EG) | extragradient · smooth convex-concave minimax, squared gradient norm | last-iterate rate | No clear effect |
| Anchoring to initial point z0 in simultaneous GD (SimGD-A) with diminishing step-sizes | SimGD-A · smooth convex-concave minimax, squared gradient norm | convergence rate and empirical speed | Hurt |
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