Group-Structured Adversarial Training

TL;DR

This paper introduces Group-Structured Adversarial Training (GSAT), a novel method to improve robustness of models against structured perturbations across samples, especially in biological and image data, using a new minimax optimization algorithm.

Contribution

The paper proposes GSAT, a new adversarial training framework for structured perturbations, and develops GDADMM, a novel optimization algorithm to solve its non-smooth minimax problem.

Findings

GSAT improves robustness against structured perturbations in biological data.

GSAT enhances model resilience in image recognition tasks.

GDADMM effectively solves the non-convex minimax optimization in GSAT.

Abstract

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.