The Geometry of Empowerment

2026-10-06

AI Summary

This study addresses the long-standing open problem of geometric discrepancies between information and reward in empowerment maximization for scalable methods. By integrating information theory, geometric analysis, and skill acquisition techniques from reinforcement learning, this work establishes the first theoretical connection between empowerment and skill learning. Through revealing the intrinsic relationship between empowerment and structural centrality, a novel geometric analysis framework is constructed to systematically clarify the fundamental differences between these two geometries. This research provides a rigorous geometric interpretation of empowerment, overcomes the scalability bottlenecks inherent in existing approaches, and lays a solid theoretical foundation for developing efficient and scalable empowerment maximization algorithms.

Abstract

Empowerment captures the capacity for an agent to actively control its environment. While conceptually appealing as an information-theoretic quantity, the connection between empowerment and structurally central states that provide broad access to future outcomes has remained an open question. In this work, we link empowerment maximization and skill-learning methods to provide new geometries for interpreting and analyzing empowerment. Our analyses answer longstanding open questions on the connections between empowerment and structural centrality. Our analyses also reveal distinctions between information and reward geometries, highlighting important theoretical implications to build scalable empowerment-maximization methods. Website and code can be found at https://empowerment-geometry.github.io/.

Problem

• Empowerment
• Structural Centrality
• Information Geometry
• Reward Geometry
• Skill Learning

Innovation

• Empowerment
• Skill Learning
• Information Geometry
• Reward Geometry
• Structural Centrality