Research map / Optimization / Nonconvex and smooth optimization
Global Convergence and Variance Reduction for a Class of Nonconvex-Nonconcave Minimax Problems
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use VR-AGDA instead of AGDA when n≤κ^9 | Finite-sum minimax problems satisfying the two-sided PL condition · Finite-sum minimax, n≤κ^9 | gradient-evaluation complexity: \mathcal{O}\left(n\kappa^3\log\frac{1}{\epsilon}\right) -> \mathcal{O}\big(n^{2/3}\kappa^3\log(1/\epsilon)\big) | Helped |
| Use VR-AGDA instead of AGDA when n≥κ^9 | Finite-sum minimax problems satisfying the two-sided PL condition · Finite-sum minimax, n≥κ^9 | gradient-evaluation complexity: \mathcal{O}\left(n\kappa^3\log\frac{1}{\epsilon}\right) -> \mathcal{O}\big((n+\kappa^9)\log(1/\epsilon)\big) | Helped |
| Use AGDA with suitable constant step sizes under the two-sided PL condition | Nonconvex-nonconcave minimax problems · Two-sided PL minimax | convergence rate: \mathcal{O}\left((1-\kappa^{-3})^t\right) | Helped |
| Use stochastic alternating updates with diminishing step sizes | Nonconvex-nonconcave minimax problems · Two-sided PL minimax | convergence rate: \mathcal{O}(\kappa^5/t) | Helped |
| Use constant step sizes for stochastic AGDA | Nonconvex-nonconcave minimax problems · Two-sided PL minimax | asymptotic error | Mixed |
| Use VR-AGDA instead of AGDA | Robust least square and LQR imitation learning · Robust least square and LQR | error versus gradient evaluations | Helped |
| Use constant-step Stoc-AGDA instead of VR-AGDA or AGDA | Robust least square · Robust least square | error versus gradient evaluations | Mixed |
| Use different learning rates for the two players in alternating updates | AGDA · Two-sided PL minimax | convergence to saddle points | Helped |
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