DeepMDP: Learning Continuous Latent Space Models for Representation Learning

Abstract: Many reinforcement learning (RL) tasks provide the agent with high-dimensional observations that can be simplified into low-dimensional continuous states. To formalize this process, we introduce the concept of a DeepMDP, a parameterized latent space model that is trained via the minimization of two tractable losses: prediction of rewards and prediction of the distribution over next latent states. We show that the optimization of these objectives guarantees (1) the quality of the latent space as a representation of the state space and (2) the quality of the DeepMDP as a model of the environment. We connect these results to prior work in the bisimulation literature, and explore the use of a variety of metrics. Our theoretical findings are substantiated by the experimental result that a trained DeepMDP recovers the latent structure underlying high-dimensional observations on a synthetic environment. Finally, we show that learning a DeepMDP as an auxiliary task in the Atari 2600 domain leads to large performance improvements over model-free RL.

• The paper introduces the DeepMDP framework to learn low-dimensional representations by minimizing discrepancies in reward and state predictions.
• It provides theoretical guarantees linking optimized loss functions to bisimulation metrics for accurate approximation of MDP dynamics.
• Empirical tests on environments like Atari demonstrate that incorporating DeepMDP significantly improves learning efficiency and overall RL performance.

DeepMDP: Learning Continuous Latent Space Models for Representation Learning

The paper "DeepMDP: Learning Continuous Latent Space Models for Representation Learning" presents a novel framework designed to enhance reinforcement learning (RL) agents through the identification and utilization of low-dimensional representations of high-dimensional state spaces. The core idea is the introduction of the DeepMDP model, a latent space construct that approximates Markov Decision Processes (MDPs) within a reduced-dimensional latent space. This approach leverages deep learning methodologies to achieve theoretically sound and empirically validated improvements in continuous state representation and RL task performance.

Key Contributions

The DeepMDP framework formalizes the concept of latent space models that minimize two key losses: the difference between predicted and actual rewards and the divergence between predicted and actual latent state distributions. These objectives ensure the model’s alignment with the underlying state space dynamics and reward structures and facilitate efficient learning processes by removing redundant or irrelevant information typically present in high-dimensional observations.

1. Latent Space Optimization: Central to their approach is the optimization of latent space models through tractable loss functions. These losses are designed to predict the immediate rewards accurately and model the distributions over subsequent latent states, ensuring the model's robustness in representing the environment's true dynamics.
2. Theoretical Guarantees: The authors provide theoretical analyses substantiating that the optimization of these losses leads to high-quality latent representations. They establish that the latent state models, when minimized under these loss functions, inherently link to bisimulation metrics, offering rigorous guarantees on representation fidelity in capturing the essential characteristics of the original task MDP, even under dimensionality reduction constraints.
3. Empirical Validation: Experimentation involves environments like Atari 2600, demonstrating that incorporating DeepMDP models as auxiliary tasks within model-free RL algorithms significantly enhances performance. Results indicate that DeepMDPs not only recover the latent structure effectively in synthetic environments but also improve representation quality, resulting in enhanced learning efficiency and policy performance across complex tasks.
4. Connections to Bisimulation: A notable theoretical insight connects DeepMDPs with bisimulation, illustrating how Wasserstein metrics used in State Aggregation within DeepMDPs enforce a form of state bisimulation. This connection underscores the fidelity of learned representations, ensuring that bisimilar states—those functionally equivalent in decision-making contexts—are aptly represented in the reduced-dimensional space.
5. Norm Maximum Mean Discrepancy Metrics: The study explores various metrics for measuring distribution discrepancies, extending beyond Wasserstein to include other Norm Maximum Mean Discrepancy metrics, which enables the selection of loss functions that best capture the underlying environmental dynamics.

Implications and Future Directions

Practically, DeepMDPs represent a potent tool for improving the efficiency of RL algorithms, making them more scalable and effective by harnessing the power of deep learning to streamline input state representations. The applications of this work span a broad spectrum of RL environments where high-dimensional observations are prevalent, notably in areas such as robotics and autonomous system controls.

Looking ahead, this research paves the way for further explorations into adaptive and hierarchical model-based learning approaches, potentially offering insights into how varying action spaces or abstraction levels can enhance decision-making capabilities. Moreover, future work might explore the development of architectures that exploit the geometric properties of latent spaces or incorporating attention and graph-based embeddings for even richer representations.

This study stands as a significant step towards bridging the gap between theoretical constructs of state space aggregation and practical, empirically-supportive implementations in RL. The dual emphasis on rigorous theoretical groundwork and demonstrative empirical testing makes it a valuable addition to the ongoing discourse in representation learning within RL.