Dissipative Gradient Descent Ascent Method: A Control Theory Inspired Algorithm for Min-max Optimization
This addresses instability issues in min-max optimization for applications like adversarial training, though it is incremental as it builds on existing GDA methods.
The paper tackled the oscillatory behavior and instability in Gradient Descent Ascent (GDA) methods for min-max optimization by introducing a dissipation term, resulting in DGDA achieving superior convergence rates compared to methods like GDA, Extra-Gradient, and Optimistic GDA.
Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings. To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized saddle function that does not strictly introduce additional convexity/concavity. We theoretically show the linear convergence of DGDA in the bilinear and strongly convex-strongly concave settings and assess its performance by comparing DGDA with other methods such as GDA, Extra-Gradient (EG), and Optimistic GDA. Our findings demonstrate that DGDA surpasses these methods, achieving superior convergence rates. We support our claims with two numerical examples that showcase DGDA's effectiveness in solving saddle point problems.