A Modified Gradient Method for Distributionally Robust Logistic Regression over the Wasserstein Ball

Abstract

In this paper, a modified conjugate gradient method under the forward-backward splitting framework is proposed to further improve the numerical efficiency for solving the distributionally robust Logistic regression model over the Wasserstein ball, which comprises two phases: in the first phase, a conjugate gradient descent step is performed, and in the second phase, an instantaneous optimization problem is formulated and solved with a trade-off minimization of the regularization term, while simultaneously staying in close proximity to the interim point obtained in the first phase. The modified conjugate gradient method is proven to attain the optimal solution of the Wasserstein distributionally robust Logistic regression model with nonsummable steplength at a convergence rate of 1/T. Finally, several numerical experiments to validate the effectiveness of theoretical analysis are conducted, which demonstrate that this method outperforms the off-the-shelf solver and the existing first-order algorithmic frameworks.