A new triple-loop algorithm, Minimax-AIPE, solves convex-concave minimax problems with tilde O(epsilon^{-4/7}) second-order oracle calls, improving the previous O(epsilon^{-2/3}).
Then ∥ ˆy − y∗∥ ≤ ∥ˆy − y∗( ˆx)∥ + ℓ1/2 µ1/2 y p ∥ ˆx − x∗∥, where we use Lemma 5.3 and y∗(x∗) = x∗ in the above inequality
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Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(\epsilon^{-4/7})$ Second-Order Oracle Complexity
A new triple-loop algorithm, Minimax-AIPE, solves convex-concave minimax problems with tilde O(epsilon^{-4/7}) second-order oracle calls, improving the previous O(epsilon^{-2/3}).