Robust Decentralized Detection and Social Learning in Tandem Networks

We study a tandem of agents who make decisions about an underlying binary hypothesis, where the distribution of the agent observations under each hypothesis comes from an uncertainty class defined by a 2-alternating capacity. We investigate both decentralized detection rules, where agents collaborate to minimize the error probability of the final agent, and social learning rules, where each agent minimizes its own local minimax error probability. We then extend our results to the infinite tandem network, and derive necessary and sufficient conditions on the uncertainty classes for the minimax error probability to converge to zero when agents know their positions in the tandem. On the other hand, when agents do not know their positions in the network, we study the cases where agents collaborate to minimize the asymptotic minimax error probability, and where agents seek to minimize their worst-case minimax error probability (over all possible positions in the tandem). We show that asymptotic learning of the true hypothesis is no longer possible in these cases, and derive characterizations for the minimax error performance.