The Limits of Learning and Planning: Minimal Sufficient Information Transition Systems

TL;DR

This paper investigates the fundamental limits of feasible policies for robots and observers by defining minimal information transition systems, providing theoretical insights into optimal sensing, planning, and policy representation.

Contribution

It introduces the concept of minimal information transition systems and proves their existence and uniqueness under broad conditions, advancing understanding of policy feasibility.

Findings

Minimal ITSs exist and are unique under certain conditions.

The theory offers new perspectives on sensor fusion and filtering.

Insights into minimal policy representations for planning tasks.

Abstract

In this paper, we view a policy or plan as a transition system over a space of information states that reflect a robot's or other observer's perspective based on limited sensing, memory, computation, and actuation. Regardless of whether policies are obtained by learning algorithms, planning algorithms, or human insight, we want to know the limits of feasibility for given robot hardware and tasks. Toward the quest to find the best policies, we establish in a general setting that minimal information transition systems (ITSs) exist up to reasonable equivalence assumptions, and are unique under some general conditions. We then apply the theory to generate new insights into several problems, including optimal sensor fusion/filtering, solving basic planning tasks, and finding minimal representations for feasible policies.