# Weak Adaptive Submodularity and Group-Based Active Diagnosis with Applications to State Estimation with Persistent Sensor Faults

## TL;DR

This paper introduces weak adaptive submodularity, a generalization of adaptive submodularity, and demonstrates its effectiveness in group-based active diagnosis for state estimation with persistent sensor faults, with near-optimal performance guarantees.

## Contribution

The paper defines weak adaptive submodularity and applies it to group-based active diagnosis, providing theoretical guarantees and practical validation in fault-tolerant state estimation.

## Key findings

- Adaptive greedy policy achieves near-optimal performance.
- Weak adaptive submodularity applies to group-based diagnosis.
- Greedy policy matches exhaustive search in experiments.

## 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.