Learning The Minimum Action Distance

Abstract: This paper presents a state representation framework for Markov decision processes (MDPs) that can be learned solely from state trajectories, requiring neither reward signals nor the actions executed by the agent. We propose learning the minimum action distance (MAD), defined as the minimum number of actions required to transition between states, as a fundamental metric that captures the underlying structure of an environment. MAD naturally enables critical downstream tasks such as goal-conditioned reinforcement learning and reward shaping by providing a dense, geometrically meaningful measure of progress. Our self-supervised learning approach constructs an embedding space where the distances between embedded state pairs correspond to their MAD, accommodating both symmetric and asymmetric approximations. We evaluate the framework on a comprehensive suite of environments with known MAD values, encompassing both deterministic and stochastic dynamics, as well as discrete and continuous state spaces, and environments with noisy observations. Empirical results demonstrate that the proposed approach not only efficiently learns accurate MAD representations across these diverse settings but also significantly outperforms existing state representation methods in terms of representation quality.

• The paper introduces the Minimum Action Distance as a novel metric that quantifies the minimum steps required for state transitions using only state trajectories.
• It employs self-supervised algorithms, MadDist and TDMadDist, to construct embedding spaces where distances align with MAD values across diverse environments.
• The framework provides an interpretable heuristic that enhances state representation, boosting policy learning in goal-conditioned reinforcement learning tasks.

Learning the Minimum Action Distance: A Novel Framework for State Representation in MDPs

The paper "Learning the Minimum Action Distance" introduces a sophisticated framework for state representation within Markov Decision Processes (MDPs), leveraging the Minimum Action Distance (MAD) as a crucial metric. This framework adopts an innovative approach by utilizing state trajectories alone, devoid of reliance on action-execution data or reward signals. The authors present a comprehensive methodology that conceptualizes MAD as the minimum step count required for state transitions, thereby encapsulating the environment's latent structure.

Core Contributions

MAD-Based State Representation: Diverging from traditional methods dependent on reward signals, this paper proposes learning MAD solely from state trajectories. This is particularly beneficial for goal-conditioned reinforcement learning and reward shaping, where MAD offers a dense and geometrically meaningful measure of progress.

Self-Supervised Embedding Space: The authors introduce a self-supervised learning process that constructs an embedding space. Within this space, distances between embedded state pairs align with MAD values, accommodating symmetric and asymmetric approximations. This embedding framework significantly enhances the representation quality across diverse environments, both deterministic and stochastic, discrete and continuous, and scenarios with noisy observations.

Methodological Innovations: Two novel algorithms, MadDist and TDMadDist, are introduced to approximate MAD efficiently and effectively. These algorithms are designed to process state trajectories, integrating asymmetric distance metrics that better encapsulate the non-linear and directional nuances of real-world environments.

Theoretical and Practical Implications

The theoretical foundation of MAD as a fundamental metric provides a lower bound on steps required for state transitions, making it invariant to probabilistic variations in transitions as long as states remain within a defined support. This aspect renders MAD suitable for transfer learning across varied environments, ensuring robustness to such changes.

From a practical standpoint, MAD serves as an interpretable heuristic that can guide reinforcement learning algorithms in goal-conditioned tasks, facilitating efficient policy learning and option discovery. The paper's experimental results further demonstrate the superiority of MAD-based representations over existing methods, portraying noteworthy improvements in correlation and consistency metrics.

Future Directions

The exploration of MAD opens several promising avenues. Investigating MAD's role in transfer learning and dynamic environments, where transition dynamics may shift while maintaining core structural characteristics, is an immediate prospect. Additionally, integrating MAD into stochastic domains as a heuristic for search algorithms could yield insights into its robustness under uncertainty.

Furthermore, while the focus has been on capturing MAD accurately, future work may explore recovering Shortest Path Distance (SPD) or identifying alternative quasimetrics that align more closely with SPD, especially in stochastic environments where MAD may serve as only a heuristic approximation.

This paper provides a refreshing perspective on state representation in MDPs, illustrating MAD's potential as a fundamental metric and paving the way for enhanced reinforcement learning methodologies. By optimizing representation learning through MAD, the paper contributes significantly to the ongoing advancement in AI and reinforcement learning research.