A Laplacian Framework for Option Discovery in Reinforcement Learning (1703.00956v2)

Abstract: Representation learning and option discovery are two of the biggest challenges in reinforcement learning (RL). Proto-value functions (PVFs) are a well-known approach for representation learning in MDPs. In this paper we address the option discovery problem by showing how PVFs implicitly define options. We do it by introducing eigenpurposes, intrinsic reward functions derived from the learned representations. The options discovered from eigenpurposes traverse the principal directions of the state space. They are useful for multiple tasks because they are discovered without taking the environment's rewards into consideration. Moreover, different options act at different time scales, making them helpful for exploration. We demonstrate features of eigenpurposes in traditional tabular domains as well as in Atari 2600 games.

• The paper introduces eigenpurposes, generating intrinsic rewards from graph Laplacian eigenvectors to derive optimal policies for RL agents.
• It demonstrates task-invariant option discovery by decoupling exploration from external rewards, enhancing versatility across varied tasks.
• Empirical results show that eigenoptions notably reduce diffusion time and accelerate reward accumulation in domains like grid worlds and Atari games.

An Analysis of Laplacian Framework for Option Discovery in Reinforcement Learning

The paper by Machado et al. proposes a method for option discovery in reinforcement learning (RL) utilizing a Laplacian framework. This approach integrates proto-value functions (PVFs) with the option discovery problem and presents a novel perspective on how options can be inherently defined by learned representations. This framework introduces the concepts of eigenpurposes and eigenbehaviors, which are essential for deriving intrinsic reward functions from PVFs and identifying optimal policies, respectively. The options derived through this framework, termed eigenoptions, enable agents to explore the state space more effectively by considering principal directions and varying temporal scales without being driven by external rewards.

Core Contributions

The paper provides several key contributions:

1. Eigenpurposes and Eigenbehaviors: The introduction of eigenpurposes as intrinsic reward functions is central to the framework. These are generated from the eigenvectors of graph Laplacians, allowing the discovery of eigenbehaviors which denote the agents' optimal policies for the intrinsic rewards.
2. Task-Invariant Option Discovery: By decoupling the discovery of options from the external reward structure, eigenoptions exhibit task independence, enabling them to be versatile across different tasks.
3. Enhanced Exploration Strategies: The paper demonstrates that eigenoptions can improve exploration strategies by operating on diverse time scales and through sequences that make it less likely for agents to revisit the same states excessively.

Empirical Evaluation

The authors validate their approach through experiments in classic RL domains like grid worlds and the Atari 2600 games. The empirical evaluation covers two main aspects:

• Exploration Metric: Through the concept of diffusion time—the expected steps needed between two random states in a random walk—the paper quantifies how eigenoptions allow more efficient exploration of the state space compared to both primitive actions and bottleneck options.
• Performance in Task Achievement: The use of eigenoptions as action choices significantly accelerates the agents' ability to accumulate rewards, demonstrating their utility in various contexts without specific task tuning.

Implications and Future Directions

The implications of this research are significant both in theoretical and practical dimensions:

• Practical Applications: By providing a mechanism to derive versatile options that enhance exploration, the paper suggests ways to address the notorious challenge of sparse rewards in RL tasks.
• Theoretical Exploration: The introduction of eigenpurposes opens new avenues to explore the theoretical underpinnings of skill and option discovery in RL, particularly how intrinsic motivations can be systematically defined and optimized.

Looking forward, potential developments could involve:

• Integration with Function Approximation: Extending the stability and efficiency of eigenoptions to domains where function approximation is required remains an open challenge.
• Adaptive Option Scale: Further investigation into the adaptability of options' temporal scales could enhance their applicability across dynamic environments.

In conclusion, the paper provides a comprehensive framework that leverages the structural properties of PVFs in RL for option discovery, furnishing a step towards a more nuanced understanding and implementation of skill acquisition and exploration in autonomous agents. The paper's insights and methodologies pave the way for robust RL systems capable of learning and performing in complex environments with minimal direct reward dependencies.