A Path-Dependent Variational Framework for Incremental Information Gathering

TL;DR

This paper introduces a novel variational framework for incremental information gathering that accounts for path-dependent, history-influenced information gain, with applications in robotics and AI exploration.

Contribution

It develops the first-order necessary optimality conditions for memory-dependent Lagrangians in path-dependent information gathering problems.

Findings

Formulation of path-dependent optimality conditions

Application to robotic exploration scenarios

Enhanced understanding of information redundancy

Abstract

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.