Robust Decentralized Detection and Social Learning in Tandem Networks

TL;DR

This paper analyzes decentralized detection and social learning in tandem networks with uncertain observation distributions, deriving conditions for error probability convergence and characterizing minimax error performance under various knowledge scenarios.

Contribution

It introduces new theoretical results on the conditions for error probability convergence and minimax error characterization in tandem networks with uncertainty.

Findings

Error probability converges to zero under certain conditions.

Agents' knowledge of their position affects learning outcomes.

Minimax error performance is characterized for different collaboration scenarios.

Abstract

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. 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.