A first-order augmented Lagrangian method for constrained minimax optimization
This work addresses constrained minimax optimization, a common challenge in machine learning and game theory, but is incremental as it builds on existing augmented Lagrangian methods.
The authors tackled constrained minimax optimization problems by proposing a first-order augmented Lagrangian method, achieving an operation complexity of O(ε^{-4} log ε^{-1}) for finding an ε-KKT solution.
In this paper we study a class of constrained minimax problems. In particular, we propose a first-order augmented Lagrangian method for solving them, whose subproblems turn out to be a much simpler structured minimax problem and are suitably solved by a first-order method developed in this paper. Under some suitable assumptions, an \emph{operation complexity} of $O(\varepsilon^{-4}\log\varepsilon^{-1})$, measured by its fundamental operations, is established for the first-order augmented Lagrangian method for finding an $\varepsilon$-KKT solution of the constrained minimax problems.