Weak Adaptive Submodularity and Group-Based Active Diagnosis with Applications to State Estimation with Persistent Sensor Faults
This work addresses state estimation with persistent sensor faults, such as in medical diagnosis or aircraft systems, by providing theoretical guarantees for efficient adaptive policies, though it is incremental as it builds on existing submodularity concepts.
The paper tackles adaptive decision-making for stochastic state estimation by introducing weak adaptive submodularity, a generalization of adaptive submodularity, and shows that an adaptive greedy policy achieves near-optimal performance in active diagnosis problems, with experiments on aircraft electrical systems demonstrating it performs equally well as exhaustive search.
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.