Generalized Kalman filter based temporal difference reinforcement learning

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: Vasos Arnaoutis, Eric Lutters, Bojana Rosić
• Venue: arXiv: cs.LG
• Published: 2026-07-22
• Collected: 2026-07-23
• URL: http://arxiv.org/abs/2607.20010v1
• PDF: https://arxiv.org/pdf/2607.20010v1
• DOI: UNKNOWN

Plain-Language Brief

The paper introduces a new reinforcement learning framework that combines conditional expectation theory with a generalized Kalman filter. This approach allows for the estimation of both the value function and its uncertainty in nonlinear models and non-Gaussian probability distributions. The method is computationally efficient due to the use of polynomial chaos expansions or ensemble-based approximations.

What the Document Says

• The paper introduces a generalized TD reinforcement learning framework based on conditional expectations.
• The value and action-value functions are treated as uncertain quantities.
• The method estimates not only the conditional expectation of the value function but also its second probabilistic moment.
• The stochastic problem is discretized using polynomial chaos expansions or ensemble-based approximations.
• The framework is demonstrated on two optimal control problems.

Key Concepts Mentioned

• reinforcement learning
• conditional expectations
• Kalman filter
• nonlinear models
• non-Gaussian probability distributions
• value function
• action-value (Q-value) functions

Claims Made by the Document

• The proposed method can accurately estimate both the value function and its associated uncertainty.
• The method extends classical Kalman-based temporal-difference learning to a broader class of stochastic systems.

Evidence Used

• Numerical examples illustrate the capability of the proposed method

Methods / Approach

• Generalized TD reinforcement learning based on conditional expectations
• Stochastic inference problem formulation
• Polynomial chaos expansions
• Ensemble-based approximations

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

The method's limitations may not be explicitly stated in the paper.

Open Questions

• How robust is the proposed method across various types of stochastic systems?
• What is the impact of using polynomial chaos expansions and ensemble-based approximations on the accuracy and efficiency of the method?

Notes for Future Q&A

May include interpretation. Labeled where it does.

The paper focuses primarily on demonstrating the proposed method, but further research could explore its robustness and impact of the discretization methods.

Raw Abstract / Excerpt

In this paper, we present a generalized temporal-difference (TD) reinforcement learning framework based on the theory of conditional expectations. The value and action-value (Q-value) functions are treated as uncertain quantities, and their estimation is formulated as a stochastic inference problem. Unlike classical Kalman-based temporal-difference learning, which relies on linear-Gaussian assumptions, the proposed formulation is derived directly from the conditional expectation framework and naturally extends to nonlinear models and non-Gaussian probability distributions. The proposed method recursively estimates not only the conditional expectation of the value function but also its second probabilistic moment, thereby quantifying the uncertainty associated with the learned value function throughout the learning process. To obtain a computationally tractable algorithm, the stochastic problem is discretized using either polynomial chaos expansions or ensemble-based approximations, providing efficient representations of the underlying random variables. The proposed framework is demonstrated on two optimal control problems: a linear mass--spring--damper system and a nonlinear heat conduction problem in a closed cavity. The numerical examples illustrate the capability of the proposed method to accurately estimate both the value function and its associated uncertainty, while extending classical Kalman-based temporal-difference learning to a broader class of stochastic systems.