Scalable Optimal Classifiers for Adversarial Settings under Uncertainty

TL;DR

This paper introduces a scalable Bayesian game framework for designing optimal classifiers in adversarial scenarios with uncertain attacker objectives, providing low-dimensional characterizations and algorithms for both offline and online settings.

Contribution

It develops a low-dimensional characterization of Bayesian Nash equilibria for adversarial classification, enabling scalable computation of approximately optimal classifiers.

Findings

Characterization of equilibria via functional threshold classifiers

Development of scalable training algorithms for offline classifiers

Design of low-regret online learning algorithms

Abstract

We consider the problem of finding optimal classifiers in an adversarial setting where the class-1 data is generated by an attacker whose objective is not known to the defender -- an aspect that is key to realistic applications but has so far been overlooked in the literature. To model this situation, we propose a Bayesian game framework where the defender chooses a classifier with no a priori restriction on the set of possible classifiers. The key difficulty in the proposed framework is that the set of possible classifiers is exponential in the set of possible data, which is itself exponential in the number of features used for classification. To counter this, we first show that Bayesian Nash equilibria can be characterized completely via functional threshold classifiers with a small number of parameters. We then show that this low-dimensional characterization enables to develop a training method to compute provably approximately optimal classifiers in a scalable manner; and to develop a learning algorithm for the online setting with low regret (both independent of the dimension of the set of possible data). We illustrate our results through simulations.