Empowerment -- an Introduction (1310.1863v2)

Abstract: This book chapter is an introduction to and an overview of the information-theoretic, task independent utility function "Empowerment", which is defined as the channel capacity between an agent's actions and an agent's sensors. It quantifies how much influence and control an agent has over the world it can perceive. This book chapter discusses the general idea behind empowerment as an intrinsic motivation and showcases several previous applications of empowerment to demonstrate how empowerment can be applied to different sensor-motor configuration, and how the same formalism can lead to different observed behaviors. Furthermore, we also present a fast approximation for empowerment in the continuous domain.

• The paper presents a novel framework that quantifies an agent's control over its environment using information theory, emphasizing task-independent empowerment.
• It applies both discrete and continuous models, employing techniques like Monte Carlo Integration to tackle computational challenges in empowerment calculations.
• It explores multi-agent dynamics and evolutionary implications, demonstrating emergent behaviors and broad applications in AI, robotics, and cognitive science.

Introduction to Empowerment

The paper "Empowerment An Introduction" provides a comprehensive exploration of the concept of Empowerment, a construct aimed at quantifying an agent's control over its environment in terms of information theory. Developed by Salge, Glackin, and Polani, this theoretical framework has gained traction due to its unique applicability across various domains, including artificial intelligence, robotics, and cognitive science.

The paper is structured into multiple sections detailing the foundations, formalism, and implications of empowerment. It further explores discrete and continuous settings, examines its applicability in multi-agent systems, and explores its theoretical underpinnings.

Fundamental Concepts and Formalism

Empowerment is positioned as a means to measure the degrees of freedom an agent possesses within its environment, serving as a proxy for 'preparedness' and, by extension, prospective fitness. This approach reinterprets the agent's control in the language of information theory, expressing it as the potential information flow or channel capacity between the agent's actions and the resulting sensor states.

Key attributes of empowerment include:

• Locality: Empowerment can be computed with knowledge of only the local dynamics, without global understanding.
• Universality: It can universally apply to any agent-environment interaction expressible probabilistically, enabling morphological transformations without losing applicability.
• Task-Independent: Empowerment isn't tied to a specific objective, making it valuable for spontaneous and general action strategies in agents.

Discrete and Continuous Empowerment

In discrete deterministic settings, empowerment is equivalent to the logarithm of the number of distinct states reachable from a given state. This aspect enables the comparison of global properties, such as graph centrality, with local empowerment estimations. Various illustrative examples, such as mazes and grid worlds, demonstrate how empowerment can emerge organically from an agent’s structural capabilities and environmental interactions.

For continuous settings, empowerment requires confronting specific challenges, like the infinite capacity of noiseless channels. Approximations like Jung’s Monte Carlo Integration and the Quasi-Linear Gaussian approach are discussed to address these challenges, each carrying its assumptions and computational costs.

Multi-Agent Systems and Evolutionary Implications

Multi-agent systems introduce an additional layer of complexity where empowerment maximization can lead to emergent behaviors reminiscent of game-theoretic dynamics. Examples discussed in the paper reveal configuration-dependent patterns reminiscent of Nash equilibria and potential zero-sum dynamics, contributing to an understanding of structured interactions within populations.

The text further examines how evolutionary processes might select for higher empowerment values, suggesting that sensor-actuator co-evolution is an indicator of optimal information channel exploitation.

Theoretical and Practical Implications

The empowerment measure hints at a plethora of potential applications both in artificial intelligence, particularly autonomous robotics, and in understanding natural behaviors. By employing task-independent utility metrics, agents might self-organize and adapt in novel surroundings without specific goal delineations.

Future work is likely to refine empowerment computations in complex, real-world environments and investigate deeper associations with learning and introspective cognitive mechanisms. Challenges remain in optimizing the computational feasibility of these empowerment calculations, particularly in real-time systems.

In conclusion, this paper serves as a pivotal resource for exploring the empowerment construct, providing an invaluable foundation for ongoing and future research in agent-environment interaction modeling.