Title: Weak Adaptive Submodularity and Group-Based Active Diagnosis with Applications to State Estimation with Persistent Sensor Faults,
Abstract: In this paper, we consider adaptive decision-making problems for stochastic
state estimation with partial observations. First, we introduce the concept of
weak adaptive submodularity, a generalization of adaptive submodularity, which
has found great success in solving challenging adaptive state estimation
problems. Then, for the problem of active diagnosis, i.e., discrete state
estimation via active sensing, we show that an adaptive greedy policy has a
near-optimal performance guarantee when the reward function possesses this
property. We further show that the reward function for group-based active
diagnosis, which arises in applications such as medical diagnosis and state
estimation with persistent sensor faults, is also weakly adaptive submodular.
Finally, in experiments of state estimation for an aircraft electrical system
with persistent sensor faults, we observe that an adaptive greedy policy
performs equally well as an exhaustive search.