Research map / Optimization / Nonconvex and smooth optimization
Efficient Algorithms for Smooth Minimax Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Combine Mirror-Prox with Nesterov accelerated gradient using implicit primal-dual updates | Strongly convex-concave minimax optimization · Strongly convex-concave minimax | primal-dual gap convergence rate: \order{k^{-1}} -> \tilde{O}(k^{-2}) | Helped |
| Use an inexact proximal-point method whose regularized subproblems are solved with DIAG | Nonconvex-concave minimax optimization · Nonconvex-concave minimax | approximate stationary point convergence rate: \order{k^{-1/5}} -> \tilde{O}(k^{-1/3}) | Helped |
| Replace the inner minimax solver with a finite convex minimax scheme | Prox-FDIAG for finite max-type objectives · Finite max-type nonconvex minimization | total gradient evaluations for an approximate stationary point: O(m/\varepsilon^4) -> \ceil[\bigg]{\frac{4^4 L (f(x_0) - f^*)}{3 \varepsilon^2}} \cdot \ceil[\bigg]{\frac{2^4 G}{\vareps | Helped |
| Decrease the inner-solver tolerance adaptively from an initial tolerance (ablation) | Prox-FDIAG · Synthetic finite max-type nonconvex minimization | convergence speed | Helped |
| Use a diminishing, non-summable but square-summable step size instead of a constant step size (ablation) | Subgradient method · Synthetic finite max-type nonconvex minimization | convergence speed: O(\frac1{\sqrt{K}}) -> O(\frac{\log(k)}{\sqrt{k}}) | Helped |
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- Last-Iterate Convergence of Single-Loop Stochastic Methods for Constrained Convex-Concave Minimax Problems (NeurIPS 2026 · similarity 0.88)
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