Research map / Optimization / Nonconvex and smooth optimization
Accelerated Primal-Dual Methods for Convex-Strongly-Concave Saddle Point Problems
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use primal acceleration in place of the LPD primal update | LPD · Convex-strongly-concave SPP with semi-linear coupling | gradient complexity: O(\tfrac{L_f}{\epsilon} + \tfrac{\|A\|}{\sqrt{\mu_g\epsilon}}) -> \mathcal{O}(\sqrt{\tfrac{L_f}{\epsilon}}) | Helped |
| Use ALPD for a general nonlinear coupling | ALPD · General nonlinear coupling SPP | gradient complexity: \mathcal{O}(\sqrt{\tfrac{L_f+L_{yy}}{\epsilon}} + \tfrac{L_{xy}}{\sqrt{\mu_g\epsilon}} + \tfrac{L_{xx}}{\epsilon}) | Mixed |
| Replace the linearized coupling term in the primal update with an inexact proximal solve | ALPD · General nonlinear coupling SPP | gradient evaluations of ∇_x φ: \mathcal{O}(\tfrac{1}{\epsilon}) -> \tilde{\mathcal{O}}(\tfrac{1}{\epsilon^{3/4}}) | Helped |
| Use ALPD instead of LPD | LPD · Linear-constraint penalty problems, p=q=2 | Gap | Helped |
| Use ALPD-prox-g instead of ALPD, applying the proximal operator of g rather than linearizing g (ablation) | ALPD · Linear-constraint penalty problems, p=q=2 | Gap | Helped |
| Use Inexact ALPD instead of ALPD | ALPD · Nonlinear-constraint penalty problems | Gap versus runtime | Helped |
| Use Inexact-ALPD-prox-g instead of ALPD-prox-g (ablation) | ALPD-prox-g · Nonlinear-constraint penalty problems | Gap versus runtime | Helped |
| Use the paper's explicit LPD step-size policy instead of the compared prior policy (ablation) | LPD · Strongly convex primal SPP with μ_g=0 | runtime performance | Helped |
Closest papers by meaning
- Accelerated Primal-Dual Gradient Method for Smooth and Convex-Concave Saddle-Point Problems with Bilinear Coupling (NeurIPS 2022 · similarity 0.95)
- On Linear Convergence in Smooth Convex-Concave Bilinearly-Coupled Saddle-Point Optimization: Lower Bounds and Optimal Algorithms (ICML 2025 · similarity 0.90)
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