Information gathered along a path is inherently submodular; the incremental amount of information gained along a path decreases due to redundant observations. In addition to submodularity, the incremental amount of information gained is a function of not only the current state but also the entire history as well. This paper presents the construction of the first-order necessary optimality conditions for memory (history-dependent) Lagrangians. Path-dependent problems frequently appear in robotics and artificial intelligence, where the state such as a map is partially observable, and information can only be obtained along a trajectory by local sensing. Robotic exploration and environmental monitoring has numerous real-world applications and can be formulated using the proposed approach.
@article{arxiv.2010.13813,
title = {A Path-Dependent Variational Framework for Incremental Information Gathering},
author = {William Clark and Maani Ghaffari},
journal= {arXiv preprint arXiv:2010.13813},
year = {2020}
}