Convergence analysis of Iterated Best Response for a trusted computation game. (April 2017)

• Record Type: Journal Article
• Authors: Bopardikar, Shaunak D.; Speranzon, Alberto; Langbort, Cédric
• Is Part Of: Automatica. Volume 78(2017)
• Page Start: 88
• Page End: 96
• Publication Date: 2017-04
• Subjects: Game theory -- Computational methods -- Adversarial machine learning -- Iterated Best Response; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.11.046
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: We introduce a game of trusted computation in which a sensor equipped with limited computing power leverages a central computer to evaluate a specified function over a large dataset, collected over time. We assume that the central computer can be under attack and we propose a strategy where the sensor retains a limited amount of the data to counteract the effect of attack. We formulate the problem as a two player game in which the sensor (defender) chooses an optimal fusion strategy using both the non-trusted output from the central computer and locally stored trusted data. The attacker seeks to compromise the computation by influencing the fused value through malicious manipulation of the data stored on the central computer. We first characterize all Nash equilibria of this game, which turn out to be dependent on parameters known to both players. Next we adopt an Iterated Best Response (IBR) scheme in which, at each iteration, the central computer reveals its output to the sensor, who then computes its best response based on a linear combination of its private local estimate and the untrusted third-party output. We characterize necessary and sufficient conditions for convergence of the IBR along with numerical results which show that the convergence conditions are relatively tight.