Generalized Kalman filter based temporal difference reinforcement learning

2026-07-22 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Engineering & Applied Sciences · Depth: Expert, quick

Summary

A new generalized temporal-difference (TD) reinforcement learning framework is introduced, based on conditional expectations theory. This framework treats value and action-value (Q-value) functions as uncertain quantities, formulating their estimation as a stochastic inference problem. Unlike traditional Kalman-based TD learning, which assumes linear-Gaussian models, this method extends to nonlinear models and non-Gaussian probability distributions. It recursively estimates both the conditional expectation and the second probabilistic moment of the value function, thereby quantifying uncertainty throughout the learning process. Computational tractability is achieved through polynomial chaos expansions or ensemble-based approximations. The framework's capabilities are demonstrated on a linear mass-spring-damper system and a nonlinear heat conduction problem, showing accurate estimation of value functions and associated uncertainty.

Key takeaway

For AI Scientists developing robust reinforcement learning agents for complex, real-world systems, this generalized Kalman filter-based TD framework offers a critical advancement. It allows you to quantify and manage uncertainty in value function estimates, moving beyond linear-Gaussian assumptions. Consider integrating this approach to enhance the reliability and safety of your agents, especially in applications involving nonlinear dynamics or non-Gaussian noise, by providing a clearer picture of decision confidence.

Key insights

This framework extends Kalman-based TD to nonlinear, non-Gaussian systems by quantifying value function uncertainty via conditional expectations.

Principles

• Value functions are uncertain quantities.
• Stochastic inference estimates value functions.
• Quantify uncertainty via second probabilistic moments.

Method

Recursively estimates conditional expectation and second probabilistic moment of value functions, discretizing the stochastic problem with polynomial chaos expansions or ensemble approximations.

In practice

• Apply to optimal control problems.
• Model nonlinear heat conduction.
• Manage uncertainty in RL value estimates.

Topics

• Reinforcement Learning
• Temporal Difference Learning
• Kalman Filter
• Uncertainty Quantification
• Stochastic Inference
• Optimal Control
• Nonlinear Systems

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.