  This paper studies the operation of multi-agent networks engaged in
multi-task decision problems under the paradigm of simultaneous learning and
adaptation. Two scenarios are considered: one in which a decision must be taken
among multiple states of nature that are known but can vary over time and
space, and another in which there exists a known "normal" state of nature and
the task is to detect unpredictable and unknown deviations from it. In both
cases the network learns from the past and adapts to changes in real time in a
multi-task scenario with different clusters of agents addressing different
decision problems. The system design takes care of challenging situations with
clusters of complicated structure, and the performance assessment is conducted
by computer simulations. A theoretical analysis is developed to obtain a
statistical characterization of the agents' status at steady-state, under the
simplifying assumption that clustering is made without errors. This provides
approximate bounds for the steady-state decision performance of the agents.
Insights are provided for deriving accurate performance prediction by
exploiting the derived theoretical results.
