Submodularity of mutual information in dynamic scenes

Determine whether mutual information retains submodularity for sequential sensor-location selection in temporally dynamic scenes or time-varying processes, as it does in static scenes, thereby establishing whether greedy (myopic) selection strategies admit near-optimality guarantees in such dynamic settings.

Background

In static environments, mutual information is known to be submodular for sensor placement, which implies that a greedy, sequential selection of sensing locations achieves performance provably close to optimal. This foundational result underpins many active perception and information-gathering algorithms by providing theoretical guarantees for myopic policies.

However, when the environment or the process of interest evolves over time, the same guarantees are not established. The temporal dynamics may break the submodularity structure or alter the objective in ways that invalidate the classic analysis, leaving open whether similar performance guarantees for greedy policies extend to dynamic scenes.