Research map / Optimization / Nonconvex and smooth optimization
Linear Last-iterate Convergence in Constrained Saddle-point Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use OGDA instead of OMWU | Matrix games over probability simplices · Random 32×32 matrix game | Last-iterate convergence speed | Helped |
| Increase the learning rate within the stable range | OGDA and OMWU · Random 32×32 matrix game | Last-iterate convergence speed | Helped |
| Set OMWU learning rate to \eta\geq11 | OMWU · Random 32×32 matrix game | Convergence: \eta\geq11 | Hurt |
| Use a constant learning rate instead of an exponentially small learning rate | OMWU · Matrix games over probability simplices with a unique equilibrium | KL divergence (last iterate): \text{KL}(\bm{z}^*,\bm{z}_t) \leq C_3(1+C_4)^{-t} | Helped |
| Use OGDA on bilinear games over polytopes without requiring a unique equilibrium | OGDA · Bilinear games over any polytope | Squared distance to equilibrium set (last iterate): \mathrm{dist}^2(\bm{z}_t, \mathcal{Z}^*) \leq 64\mathrm{dist}^2(\zp_1, \mathcal{Z}^*)(1+C_5)^{-t} | Helped |
| Use OGDA when SP-MS holds with \beta > 0 rather than \beta = 0 | OGDA · SP-MS problems with \beta > 0 | Squared distance to equilibrium set (last iterate): t^{-\frac{1}{\beta}} | Mixed |
| Use OGDA on a bilinear game with a curved, non-polytope feasible set | OGDA · Bilinear game on curved feasible regions | Squared distance to equilibrium set: \Omega(1/t^2) | Hurt |
| Apply OGDA rather than OMWU to the strongly-convex-strongly-concave example | OGDA and OMWU · Strongly-convex-strongly-concave game | Convergence speed | Helped |
| Remove the unique-equilibrium requirement for OGDA | OGDA · Bilinear games over polytopes | Last-iterate convergence rate | Helped |
| Initialize OGDA outside a small neighborhood of the unique equilibrium | OGDA · Matrix games | Last-iterate convergence rate | Helped |
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