Robust optimization for adversarial learning with finite sample complexity guarantees

Decision making and learning under uncertainty, especially with adversarial attacks, is crucial for reliable operations. This paper introduces a novel adversarial training method for robust linear and nonlinear classifiers, inspired by Support Vector Machine (SVM) margins. We derive finite sample complexity bounds for binary and multi-class classifiers, which align with those of natural classifiers. Our algorithm uses Linear Programming (LP) and Second Order Cone Programming (SOCP) for linear and nonlinear models, respectively. Experiments on MNIST and CIFAR10 datasets demonstrate performance comparable to state-of-the-art methods, without requiring adversarial examples during training. Our approach provides a robust framework for enhancing classifier resilience against adversaries.