Detection Games under Fully Active Adversaries

Area of Science:

• Information Theory
• Statistical Inference
• Game Theory

Background:

• Binary hypothesis testing involves a defender distinguishing between two data sources (P0, P1).
• Previous adversarial models considered partially active attackers (active under one hypothesis only).
• This work addresses a fully active attacker, distorting data under both hypotheses.

Purpose of the Study:

• To analyze a novel adversarial setup with a fully active attacker in binary hypothesis testing.
• To model the defender-attacker interaction as a game (Neyman-Pearson and Bayesian games).
• To characterize optimal attack strategies and derive the defender's best achievable performance.

Main Methods:

• Game-theoretic modeling of the defender-attacker interaction.
• Analysis of two game versions: Neyman-Pearson and Bayesian games.
• Characterization of asymptotically dominant and universal attack strategies.

Main Results:

• Identified a dominant and universal attack strategy, independent of source distributions (P0, P1).
• Derived the defender's best achievable performance by analyzing equilibrium payoffs.
• Characterized conditions for source distinguishability under given distortion levels.

Conclusions:

• The fully active attacker model presents unique challenges in hypothesis testing.
• A universal and dominant attack strategy significantly impacts detection performance.
• Understanding these adversarial dynamics is crucial for determining source distinguishability limits.