MASAGE: Model-Agnostic Sequential and Adaptive Game Estimation

Zero-sum games have been used to model cybersecurity scenarios between an attacker and a defender. However, unknown and uncertain environments have made it difficult to rely on a prescribed zero-sum game to capture the interactions between the players. In this work, we aim to estimate and recover an unknown matrix game that encodes the uncertainties of nature and opponent based on the knowledge of historical games and the current observations of game outcomes. The proposed approach effectively transfers the past experiences that are encoded as expert games to estimate and inform future game plays. We formulate the game knowledge transfer and estimation problem as a sequential least-square problem. We characterize the structural properties of the problem and show that the non-convex problem has well-behaved gradient and Hessian under mild assumptions. We propose gradient-based methods to enable dynamic and adaptive estimation of the unknown game. A case study is used to corroborate the results and illustrate the behavior of the proposed algorithm.