Uncertainty Representations in State-Space Layers for Deep Reinforcement Learning under Partial Observability (2409.16824v2)

Abstract: Optimal decision-making under partial observability requires reasoning about the uncertainty of the environment's hidden state. However, most reinforcement learning architectures handle partial observability with sequence models that have no internal mechanism to incorporate uncertainty in their hidden state representation, such as recurrent neural networks, deterministic state-space models and transformers. Inspired by advances in probabilistic world models for reinforcement learning, we propose a standalone Kalman filter layer that performs closed-form Gaussian inference in linear state-space models and train it end-to-end within a model-free architecture to maximize returns. Similar to efficient linear recurrent layers, the Kalman filter layer processes sequential data using a parallel scan, which scales logarithmically with the sequence length. By design, Kalman filter layers are a drop-in replacement for other recurrent layers in standard model-free architectures, but importantly they include an explicit mechanism for probabilistic filtering of the latent state representation. Experiments in a wide variety of tasks with partial observability show that Kalman filter layers excel in problems where uncertainty reasoning is key for decision-making, outperforming other stateful models.

• The paper introduces a novel Kalman filter layer for closed-form Gaussian inference, addressing uncertainty in deep reinforcement learning under partial observability.
• It demonstrates a scalable method by integrating the KF layer with standard neural components, achieving superior performance in tasks like best arm identification and continuous control.
• Experimental evaluations across various POMDPs show enhanced memory capabilities, improved adaptability, and robust decision-making in uncertain environments.

Uncertainty Representations in State-Space Layers for Deep Reinforcement Learning under Partial Observability

The paper "Uncertainty Representations in State-Space Layers for Deep Reinforcement Learning under Partial Observability" by Carlos E. Luis et al. presents a novel approach to enhancing reinforcement learning (RL) architectures by incorporating probabilistic inference mechanisms into state-space models (SSMs) to handle partial observability in decision-making tasks.

Overview

The authors address a significant challenge in reinforcement learning under partial observability: the inability of many existing architectures (e.g., RNNs, deterministic SSMs, transformers) to incorporate uncertainty in their latent state representations. This limitation can undermine decision-making where reasoning about uncertainty is crucial.

Inspired by recent advances in probabilistic world models, the paper introduces a standalone Kalman filter (KF) layer. This layer performs closed-form Gaussian inference in linear state-space models and can be integrated end-to-end within a model-free RL architecture. The KF layer offers an explicit mechanism for probabilistic filtering of latent states and can replace existing recurrent layers in standard architectures.

Contributions and Methodology

The main contributions of this work are:

1. Kalman Filter Layer: The introduction of a KF layer that performs efficient probabilistic filtering via closed-form Gaussian inference. This layer operates with a parallel scan technique, scaling logarithmically with sequence length. Its design allows it to be a drop-in replacement for other recurrent layers in RL architectures.
2. Implementation and Integration: The KF layer can be stacked and combined with other neural network components, such as residual connections and normalization layers, to create more complex sequence models.
3. Evaluation in Varied Tasks: Extensive experiments in various partially observable Markov decision processes (POMDPs) demonstrate the performance advantages of the KF layers, particularly in tasks where probabilistic reasoning is paramount for decision-making.

Experimental Results

The paper evaluates the proposed KF layer across different environments, comparing it with other sequence models like GRUs, deterministic SSMs (vSSM), and transformers (vTransformer). Key findings include:

1. Probabilistic Reasoning and Adaptation:
   • In the Best Arm Identification task, where an agent must balance between gathering more information and making conclusive decisions, the KF-enhanced models demonstrated superior performance. The vSSM+KF model particularly showed higher returns and better adaptability to different noise distributions compared to other stateful models.
2. Continuous Control under Observation Noise:
   • Across nine environments from the DeepMind Control suite subjected to observation noise, the KF layers' integration resulted in significant performance improvements. The vSSM+KF model maintained performance close to the oracle under full observability and showed robustness across different noise levels.
3. General Memory Capabilities:
   • In the POPGym benchmark, designed to test long-term memory and recall, vSSM+KF consistently performed well, highlighting its general-purpose applicability across various POMDPs. Notably, the model showed particular strengths in tasks requiring efficient memory recall.

Theoretical and Practical Implications

The introduction of the KF layer addresses a critical gap in RL under partial observability by embedding an inductive bias for probabilistic reasoning directly into the sequence model. Practically, this approach may improve RL applications in complex domains like robotics and autonomous systems, where reasoning about uncertainty and adaptation is vital for robust decision-making. The efficient implementation using parallel scans ensures that the approach is scalable and suitable for real-time applications.

Future Research Directions

The paper opens several avenues for future research:

• Model Enlargement and Complexity: Investigating the performance of larger and more complex models incorporating KF layers could reveal new capabilities and optimization strategies.
• Task-Specific Design Adjustments: Exploring different configurations of KF layers, such as time-varying process noise or including posterior covariance in the output features, could further enhance model performance in specific tasks or environments.
• Real-World Applications: Extending evaluations to more complex, high-dimensional POMDPs could provide insights into the KF layer's applicability and benefits in real-world scenarios.

Conclusion

This work contributes substantially to the reinforcement learning community by proposing and empirically validating a novel method for incorporating uncertainty representations via Kalman filter layers. This approach enhances decision-making in partially observable environments, paving the way for more resilient and adaptable RL systems. The reliance on established filtering techniques provides robust theoretical grounding and practical advantages, making it a promising direction for future research and applications in AI.