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Scalable Optimal Classifiers for Adversarial Settings under Uncertainty

Benjamin Roussillon 1 Patrick Loiseau 1 
1 POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
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 us 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.
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https://hal.inria.fr/hal-03360526
Contributor : Patrick Loiseau Connect in order to contact the contributor
Submitted on : Thursday, September 30, 2021 - 5:49:00 PM
Last modification on : Wednesday, July 6, 2022 - 4:22:54 AM
Long-term archiving on: : Friday, December 31, 2021 - 9:03:16 PM

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  • HAL Id : hal-03360526, version 1

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Benjamin Roussillon, Patrick Loiseau. Scalable Optimal Classifiers for Adversarial Settings under Uncertainty. GameSec 2021 - 12th Conference on Decision and Game Theory for Security, Oct 2021, Prague, Czech Republic. pp.1-20. ⟨hal-03360526⟩

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