Conjectural Online Learning with First-order Beliefs in Asymmetric Information Stochastic Games

Stochastic games arise in many complex socio-technical systems, such as cyber-physical systems and IT infrastructures, where information asymmetry presents challenges for decision-making entities (players). Existing computational methods for asymmetric information stochastic games (AISG) are primarily offline, targeting special classes of AISGs to avoid belief hierarchies, and lack online adaptability to deviations from equilibrium. To address this limitation, we propose a conjectural online learning (COL), a learning scheme for generic AISGs. COL, structured as a forecaster-actor-critic (FAC) architecture, utilizes first-order beliefs over the hidden states and subjective forecasts of the opponent's strategies. Against the conjectured opponent, COL updates strategies in an actor-critic approach using online rollout and calibrates conjectures through Bayesian learning. We prove that conjecture in COL is asymptotically consistent with the information feedback in the sense of a relaxed Bayesian consistency. The resulting empirical strategy profile converges to the Berk-Nash equilibrium, a solution concept characterizing rationality under subjectivity. Experimental results from an intrusion response use case demonstrate COL's superiority over state-of-the-art reinforcement learning methods against nonstationary attacks.