Empowerment for Continuous Agent-Environment Systems (1201.6583v1)

Abstract: This paper develops generalizations of empowerment to continuous states. Empowerment is a recently introduced information-theoretic quantity motivated by hypotheses about the efficiency of the sensorimotor loop in biological organisms, but also from considerations stemming from curiosity-driven learning. Empowemerment measures, for agent-environment systems with stochastic transitions, how much influence an agent has on its environment, but only that influence that can be sensed by the agent sensors. It is an information-theoretic generalization of joint controllability (influence on environment) and observability (measurement by sensors) of the environment by the agent, both controllability and observability being usually defined in control theory as the dimensionality of the control/observation spaces. Earlier work has shown that empowerment has various interesting and relevant properties, e.g., it allows us to identify salient states using only the dynamics, and it can act as intrinsic reward without requiring an external reward. However, in this previous work empowerment was limited to the case of small-scale and discrete domains and furthermore state transition probabilities were assumed to be known. The goal of this paper is to extend empowerment to the significantly more important and relevant case of continuous vector-valued state spaces and initially unknown state transition probabilities. The continuous state space is addressed by Monte-Carlo approximation; the unknown transitions are addressed by model learning and prediction for which we apply Gaussian processes regression with iterated forecasting. In a number of well-known continuous control tasks we examine the dynamics induced by empowerment and include an application to exploration and online model learning.

• The paper extends empowerment to continuous systems by approximating high-dimensional integrals with Monte Carlo methods.
• The paper employs Gaussian process regression to iteratively learn unknown state dynamics for autonomous online learning.
• The paper validates the approach across continuous control tasks, achieving performance near RMAX with improved sample efficiency.

Overview of Empowerment in Continuous Agent-Environment Systems

The paper "Empowerment for Continuous Agent-Environment Systems" by Tobias Jung, Daniel Polani, and Peter Stone, extends the concept of empowerment from discrete and small-scale agent-environment systems to continuous systems with initially unknown state transition probabilities. Empowerment, an information-theoretic measure introduced earlier, quantifies an agent’s influence over its environment that is concurrently observable through the agent's sensors. This measure combines elements of controllability and observability and has been posited to be useful as an intrinsic reward mechanism, enabling autonomous agents to self-organize and learn without requiring external rewards.

In this paper, the researchers aim to address the crucial issue of transitioning empowerment to continuous vector-valued state spaces, a step forward from the earlier, more limited discrete implementations. By utilizing Monte Carlo approximations, state transitions are estimated under continuous state spaces, while Gaussian process (GP) regression is employed for predicting unknown state transition probabilities. This allows the empowerment framework to be applied to systems where state transition knowledge is not a priori available to the agent.

Key Developments and Results

1. Extension to Continuous Systems: The paper tackles the complexities inherent in applying empowerment to continuous systems. This is achieved by approximating the necessary integrals using Monte Carlo methods. The continuous nature of state spaces adds computational complexity due to the need for accurate integration over high-dimensional areas, which Monte Carlo methods manage comparably well.
2. Model Learning via Gaussian Processes: Gaussian processes are leveraged for model learning, allowing the agent to predict state transitions iteratively. This predictive model enables the extension of empowerment to systems where transition dynamics are initially unknown, thereby facilitating online learning as the agent interacts with its environment.
3. Validation in Continuous Control Tasks: The paper reinforces its theoretical propositions through empirical testing in several established continuous control tasks, such as inverted pendulum, bicycle riding, and acrobot. These domains are typical testbeds to evaluate autonomous agent behavior and model learning algorithms. The results across these tasks demonstrated that empowerment could indeed guide the agent to states that align with those generally deemed as goal states when external criteria are considered.
4. Comparison with RMAX: The paper also juxtaposes the results obtained using empowerment with those from the RMAX model-based reinforcement learning algorithm. The findings show that while empowerment did not explicitly optimize for the task-specific reward structure, it nonetheless achieved performance close to RMAX. Furthermore, empowerment required fewer samples for learning, showcasing efficiency in exploration and learning.

Implications and Future Perspectives

The extension of empowerment to continuous systems represents an important development in creating self-driven agents capable of intuitive and generalized behavior. The approach's intrinsic nature indicates potential for application in complex, real-world scenarios where the precise dynamics of environments are unspecified or evolve over time. This property aligns with the rising imperative for scalable autonomous systems learning and evolving in an increasingly data-driven world.

Future research may explore the application of empowerment across diverse domains, into vectors such as higher-dimensional action spaces, or investigate computational optimizations and approximations such as improved empirical strategies for calculating action outcomes and empowerment gradients. The practical advancement of scalable implementations will likely rely on such optimizations, particularly in robotic and real-time simulation environments. Furthermore, integrating empowerment with other machine learning methodologies, potentially enriching interpretability and flexibility, might unlock even broader applications in AI.