Research map / Optimization / Nonconvex and smooth optimization
Adaptive and Universal Algorithms for Variational Inequalities with Optimal Convergence
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Set adaptive step sizes using operator-value differences rather than iterate movement | AdaPEG scalar on bounded-domain variational inequalities · Non-smooth, smooth, and stochastic settings | convergence rate: Ω(\sqrt{\ln T}) | Helped |
| Use one operator evaluation per iteration instead of two (ablation) | AdaPEG and its 2-call variants · Bilinear saddle-point experiments | performance | No clear effect |
| Remove the additional \((\gamma_t-\gamma_{t-1})\|u-x_t\|^2\) term from the update for z_t (ablation) | AdaPEG · Bilinear problems with bounded feasible domain | performance | No clear effect |
| Remove the additional \((\gamma_t-\gamma_{t-1})\|u-x_t\|^2\) term from the update for z_t (ablation) | AdaPEG · Unconstrained stochastic bilinear problems | performance | Mixed |
| Use per-coordinate step sizes instead of a scalar step size (ablation) | AdaPEG · Some bilinear saddle-point experiments | performance | Helped |
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