Robust detection and social learning in tandem networks

We consider a binary hypothesis testing problem in a tandem network where the distribution of the agent observations under each hypothesis comes from an uncertainty class. When agents know their positions in the tandem, and the contamination of the uncertainty classes are non-zero, we show that asymptotic learning of the true hypothesis under social learning is not possible even when the log likelihood ratio of the nominal distributions of the uncertainty classes is unbounded. Furthermore, asymptotic learning in social learning is achievable if and only if the uncertainty classes contamination converge to zero. When agents do not know their positions, the minimax error probability is bounded from zero, and we provide tight bounds for it.