Dynamic Cheap Talk for Robust Adversarial Learning

Abstract

Robust adversarial learning is considered in the context of closed-loop control with adversarial signaling in this paper. Due to the nature of incomplete information of the control agent about the environment, the belief-dependent signaling game formulation is introduced in the dynamic system and a dynamic cheap talk game is formulated with belief-dependent strategies for both players. We show that the dynamic cheap talk game can further be reformulated as a particular stochastic game, where the states are beliefs of the environment and the actions are the adversarial manipulation strategies and control strategies. Furthermore, the bisimulation metric is proposed and studied for the dynamic cheap talk game, which provides an upper bound on the difference between values of different initial beliefs in the zero-sum equilibrium.