The Faulty GPS Problem: Shortest Time Paths in Networks with Unreliable Directions

TL;DR

This paper studies optimal motion planning in networks with unreliable directional guidance, proposing strategies to minimize expected travel time when GPS suggestions are probabilistically trustworthy, with applications to autonomous agents and AI trust.

Contribution

It introduces the Faulty GPS Problem, analyzing how to optimally trust unreliable directional signals in network navigation to minimize expected travel time.

Findings

Derived optimal trust probabilities q(q,p) for shortest expected time paths.

Extended the model to node-dependent trust probabilities and multi-agent treasure hunts.

Connected the problem to AI trust issues and biological navigation systems.

Abstract

This paper optimizes motion planning when there is a known risk that the road choice suggested by a Satnav (GPS) is not on a shortest path. At every branch node of a network Q, a Satnav (GPS) points to the arc leading to the destination, or home node, H - but only with a high known probability p. Always trusting the Satnav's suggestion may lead to an infinite cycle. If one wishes to reach H in least expected time, with what probability q=q(Q,p) should one trust the pointer (if not, one chooses randomly among the other arcs)? We call this the Faulty Satnav (GPS) Problem. We also consider versions where the trust probability q can depend on the degree of the current node and a `treasure hunt' where two searchers try to reach H first. The agent searching for H need not be a car, that is just a familiar example -- it could equally be a UAV receiving unreliable GPS information. This problem has its origin not in driver frustration but in the work of Fonio et al (2017) on ant navigation, where the pointers correspond to pheromone markers pointing to the nest. Neither the driver or ant will know the exact process by which a choice (arc) is suggested, which puts the problem into the domain of how much to trust an option suggested by AI.