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Adversarial examples are a pervasive phenomenon of machine learning modelswhere seemingly imperceptible perturbations to the input lead tomisclassifications for otherwise statistically accurate models. In this paperwe study how the choice of optimization algorithm influences the robustness ofthe resulting classifier to adversarial examples. Specifically we show anexample of a learning problem for which the solution found by adaptiveoptimization algorithms exhibits qualitatively worse robustness propertiesagainst both $L_{2}$- and $L_{\infty}$-adversaries than the solution found bynon-adaptive algorithms. Then we fully characterize the geometry of the losslandscape of $L_{2}$-adversarial training in least-squares linear regression.The geometry of the loss landscape is subtle and has important consequences foroptimization algorithms. Finally we provide experimental evidence whichsuggests that non-adaptive methods consistently produce more robust models thanadaptive methods.

Adaptive versus Standard Descent Methods and Robustness Against Adversarial Examples