Group-Structured Adversarial Training
This work addresses robustness against structured perturbations for machine learning models, particularly in domains like computational biology, but it is incremental as it builds on existing adversarial training methods.
The paper tackles the problem of adversarial training's suboptimal performance against structured perturbations across samples, such as group-sparse shifts common in biological data, by introducing Group-Structured Adversarial Training (GSAT) and demonstrating its effectiveness in improving robustness for image recognition and computational biology datasets.
Robust training methods against perturbations to the input data have received great attention in the machine learning literature. A standard approach in this direction is adversarial training which learns a model using adversarially-perturbed training samples. However, adversarial training performs suboptimally against perturbations structured across samples such as universal and group-sparse shifts that are commonly present in biological data such as gene expression levels of different tissues. In this work, we seek to close this optimality gap and introduce Group-Structured Adversarial Training (GSAT) which learns a model robust to perturbations structured across samples. We formulate GSAT as a non-convex concave minimax optimization problem which minimizes a group-structured optimal transport cost. Specifically, we focus on the applications of GSAT for group-sparse and rank-constrained perturbations modeled using group and nuclear norm penalties. In order to solve GSAT's non-smooth optimization problem in those cases, we propose a new minimax optimization algorithm called GDADMM by combining Gradient Descent Ascent (GDA) and Alternating Direction Method of Multipliers (ADMM). We present several applications of the GSAT framework to gain robustness against structured perturbations for image recognition and computational biology datasets.