Accelerated Margin Maximization Rates for Generic and Adversarially Robust Optimization Methods

Generic optimization methods such as mirror descent and steepest descent can achieve significantly faster margin maximization rates compared to previous results, by transforming the optimization problem into an equivalent regularized bilinear game that can be solved using online learning algorithms. Similarly, adversarial training methods can also attain faster margin maximization rates that match the best known rates for optimization on clean data.