Convergence of two-timescale gradient descent ascent dynamics: finite-dimensional and mean-field perspectives
It addresses convergence issues in min-max optimization for machine learning and game theory, but appears incremental as it builds on existing GDA methods with specific analyses.
The paper analyzes the convergence behavior of two-timescale gradient descent-ascent (GDA) in min-max games, showing long-time convergence in finite-dimensional quadratic games under near quasi-static regimes and convergence in mean-field settings using a finite-scale ratio.
The two-timescale gradient descent-ascent (GDA) is a canonical gradient algorithm designed to find Nash equilibria in min-max games. We analyze the two-timescale GDA by investigating the effects of learning rate ratios on convergence behavior in both finite-dimensional and mean-field settings. In particular, for finite-dimensional quadratic min-max games, we obtain long-time convergence in near quasi-static regimes through the hypocoercivity method. For mean-field GDA dynamics, we investigate convergence under a finite-scale ratio using a mixed synchronous-reflection coupling technique.