Generalized Gaussian Temporal Difference Error for Uncertainty-aware Reinforcement Learning

2026-07-27 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

This paper introduces a novel framework for generalized Gaussian error modeling in deep reinforcement learning, applicable to both discrete and continuous control settings. It addresses the limitations of conventional uncertainty-aware temporal difference (TD) learning methods that rely on simplistic zero-mean Gaussian distribution assumptions for TD errors. The framework enhances error distribution modeling by incorporating higher-order moments, specifically kurtosis, to improve estimation and mitigation of aleatoric uncertainty. It also proposes a theoretically grounded weighting scheme and enhances batch inverse variance weighting with bias reduction and kurtosis considerations to address epistemic uncertainty. Extensive experimental evaluations using policy gradient algorithms like SAC and PPO on benchmarks such as MuJoCo and Gymnasium demonstrate consistent efficacy and significant performance improvements.

Key takeaway

For AI Scientists and Machine Learning Engineers developing robust RL agents in noisy or complex environments, you should move beyond traditional Gaussian assumptions for Temporal Difference errors. By adopting Generalized Gaussian Distribution (GGD) error modeling, which accounts for kurtosis, and implementing Batch Inverse Error Variance (BIEV) regularization, you can achieve more accurate uncertainty quantification. This approach enhances model stability, improves sample efficiency, and leads to significant performance gains in both discrete and continuous control tasks.

Key insights

Generalized Gaussian error modeling improves uncertainty estimation in deep RL by accounting for TD error distribution shape.

Principles

• Conventional Gaussian assumptions for TD errors are overly restrictive and compromise sample efficiency.
• Kurtosis significantly influences the reliability of uncertainty estimation and variance estimates.
• Aleatoric uncertainty is negatively proportional to the GGD shape parameter β on an exponential scale.

Method

The method uses a GGD-NLL loss with a beta head to model aleatoric uncertainty and a batch inverse error variance (BIEV) weighting scheme for epistemic uncertainty, incorporating kurtosis for robustness.

In practice

• Employ a beta head for Generalized Gaussian Distribution (GGD) error modeling in RL agents.
• Utilize risk-averse weighting (ωᴿᵃₜ = Qᵇₜ) to learn from less spread-out samples.
• Apply Batch Inverse Error Variance (BIEV) regularization to down-weight high-variance samples.

Topics

• Reinforcement Learning
• Uncertainty Quantification
• Generalized Gaussian Distribution
• Temporal Difference Learning
• Aleatoric Uncertainty
• Epistemic Uncertainty
• Policy Gradient Algorithms

Code references

• ait-lab/ggtde

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.