A Path-Dependent Variational Framework for Incremental Information Gathering
It addresses path-dependent optimization in robotics and AI for applications such as robotic exploration and environmental monitoring, but the work appears incremental as it builds on existing variational frameworks.
The paper tackled the problem of incremental information gathering along paths, which is submodular and history-dependent, by developing first-order necessary optimality conditions for memory Lagrangians. This provides a theoretical framework applicable to robotics and AI tasks like exploration and monitoring.
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.