Detection Games Under Fully Active Adversaries

TL;DR

This paper investigates a binary hypothesis testing game with a fully active adversary who distorts sequences under both hypotheses to maximize detection errors, providing a game-theoretic analysis and characterizing optimal attack strategies and source distinguishability.

Contribution

It introduces a novel fully active adversarial model in hypothesis testing and characterizes asymptotically dominant attack strategies and source distinguishability conditions.

Findings

Identified a universal asymptotically dominant attack strategy.

Characterized the equilibrium performance and error tradeoffs.

Derived conditions for source distinguishability under distortion constraints.

Abstract

We study a binary hypothesis testing problem in which a defender must decide whether or not a test sequence has been drawn from a given memoryless source $P_0$ whereas, an attacker strives to impede the correct detection. With respect to previous works, the adversarial setup addressed in this paper considers an attacker who is active under both hypotheses, namely, a fully active attacker, as opposed to a partially active attacker who is active under one hypothesis only. In the fully active setup, the attacker distorts sequences drawn both from $P_0$ and from an alternative memoryless source $P_1$, up to a certain distortion level, which is possibly different under the two hypotheses, in order to maximize the confusion in distinguishing between the two sources, i.e., to induce both false positive and false negative errors at the detector, also referred to as the defender. We model the defender-attacker interaction as a game and study two versions of this game, the Neyman-Pearson game and the Bayesian game. Our main result is in the characterization of an attack strategy that is asymptotically both dominant (i.e., optimal no matter what the defender's strategy is) and universal, i.e., independent of $P_0$ and $P_1$. From the analysis of the equilibrium payoff, we also derive the best achievable performance of the defender, by relaxing the requirement on the exponential decay rate of the false positive error probability in the Neyman--Pearson setup and the tradeoff between the error exponents in the Bayesian setup. Such analysis permits to characterize the conditions for the distinguishability of the two sources given the distortion levels.