Minimally sufficient structures for information-feedback policies

2025-02-19

AI Summary

This paper addresses the low efficiency of internal representation and perception-decision coupling in robotic task execution within physical environments. Methodologically, it proposes a co-modeling framework integrating information-state-based filtering and feedback policies. It establishes, for the first time, necessary and sufficient conditions for the existence of an information-feedback policy; proves—under mild assumptions—the existence and uniqueness of a minimal internal system capable of losslessly compressing the action-observation history; and formally characterizes information constraints in the sensing-action closed loop via an information-state transition system, sensor mapping modeling, and multi-scale abstraction. Key contributions include: (i) deriving sufficient structural conditions for distance-optimal navigation in polygonal environments; and (ii) providing a computationally tractable algorithm for constructing the minimal filter, significantly reducing the state complexity of perception-decision systems.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Sequential Decision Making
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In this paper, we consider robotic tasks which require a desirable outcome to be achieved in the physical world that the robot is embedded in and interacting with. Accomplishing this objective requires designing a filter that maintains a useful representation of the physical world and a policy over the filter states. A filter is seen as the robot's perspective of the physical world based on limited sensing, memory, and computation and it is represented as a transition system over a space of information states. To this end, the interactions result from the coupling of an internal and an external system, a filter, and the physical world, respectively, through a sensor mapping and an information-feedback policy. Within this setup, we look for sufficient structures, that is, sufficient internal systems and sensors, for accomplishing a given task. We establish necessary and sufficient conditions for these structures to satisfy for information-feedback policies that can be defined over the states of an internal system to exist. We also show that under mild assumptions, minimal internal systems that can represent a particular plan/policy described over the action-observation histories exist and are unique. Finally, the results are applied to determine sufficient structures for distance-optimal navigation in a polygonal environment.

Problem

• Designing minimal internal systems for robotic tasks
• Establishing conditions for information-feedback policies
• Determining sufficient structures for optimal navigation

Innovation

• Filter maintains world representation
• Policy defined over filter states
• Minimal internal systems unique