  Machine-learning techniques are widely used in security-related applications,
like spam and malware detection. However, in such settings, they have been
shown to be vulnerable to adversarial attacks, including the deliberate
manipulation of data at test time to evade detection. In this work, we focus on
the vulnerability of linear classifiers to evasion attacks. This can be
considered a relevant problem, as linear classifiers have been increasingly
used in embedded systems and mobile devices for their low processing time and
memory requirements. We exploit recent findings in robust optimization to
investigate the link between regularization and security of linear classifiers,
depending on the type of attack. We also analyze the relationship between the
sparsity of feature weights, which is desirable for reducing processing cost,
and the security of linear classifiers. We further propose a novel octagonal
regularizer that allows us to achieve a proper trade-off between them. Finally,
we empirically show how this regularizer can improve classifier security and
sparsity in real-world application examples including spam and malware
detection.
