GDA-AM: ON THE EFFECTIVENESS OF SOLVING MIN-IMAX OPTIMIZATION VIA ANDERSON MIXING.

Area of Science:

• Machine Learning
• Optimization Theory
• Deep Learning

Background:

• Many machine learning algorithms, including generative adversarial networks (GANs), are formulated as minimax optimization problems.
• Gradient Descent Ascent (GDA) is a common but often unstable method for solving these problems, sometimes converging to suboptimal solutions.

Purpose of the Study:

• To develop a more stable and efficient framework for solving minimax optimization problems.
• To address the convergence issues of standard Gradient Descent Ascent (GDA) in simultaneous and alternating update settings.

Main Methods:

• Proposing GDA-AM, a new framework that treats GDA dynamics as a fixed-point iteration.
• Applying Anderson Mixing to accelerate and stabilize the convergence to local minimax points.

Main Results:

• Theoretical proof of global convergence for bilinear problems under specific conditions.
• Empirical validation showing GDA-AM effectively solves diverse minimax problems.
• Demonstrated improvements in adversarial training across multiple datasets.

Conclusions:

• GDA-AM offers a robust solution for minimax optimization challenges in machine learning.
• The framework enhances both the stability and convergence speed of GDA-based methods.
• This approach shows significant promise for advancing adversarial training techniques.