Generalized Kalman filter based temporal difference reinforcement learning

• URL: http://arxiv.org/abs/2607.20010v2
• Date: Thu, 23 Jul 2026 08:57:32 GMT
• Title: Generalized Kalman filter based temporal difference reinforcement learning
• Abstract summary: We present a generalized temporal-difference (TD) reinforcement learning framework based on the theory of conditional expectations.<n>Unlike classical Kalman-based temporal-difference learning, which relies on linear-Gaussian assumptions, the proposed formulation is derived directly from the conditional expectation framework.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Non-Parametric Rehearsal Learning via Conditional Mean Embeddings [88.89267783967263]
  We propose a non-parametric rehearsal learning approach for textitavoiding undesired future (AUF) problems.<n>Specifically, we use kernel machinery to reformulate the AUF objective into a unified representation that disentangles desirability modeling from action-induced distributional changes.
  arXiv  Detail & Related papers  (2026-05-09T15:30:52Z)
• Extraction of informative statistical features in the problem of forecasting time series generated by It{ô}-type processes [65.01025489527173]
  We use the parameters of statistically adjusted mixture-type models of the observed regularities of the behavior of the time series.<n>We show that the use of additional statistical features improves the prediction.
  arXiv  Detail & Related papers  (2026-04-18T06:31:21Z)
• Malliavin Calculus with Weak Derivatives for Counterfactual Stochastic Optimization [16.179901221618156]
  We study counterfactual optimization of conditional loss functionals under misspecified noisy gradient information.<n>We show using Malliavin calculus that the conditional loss functional of a diffusion process admits an exact representation as a Skorohod integral, yielding variance comparable to classical Monte-Carlo.
  arXiv  Detail & Related papers  (2025-09-30T21:37:54Z)
• A Functional Model Method for Nonconvex Nonsmooth Conditional Stochastic Optimization [0.0]
  We consider optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector. We propose a specialized singlescale method for non constrained learning problems with a smooth outer function and a different conditional inner function.
  arXiv  Detail & Related papers  (2024-05-17T14:35:50Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Semi-Parametric Inference for Doubly Stochastic Spatial Point Processes: An Approximate Penalized Poisson Likelihood Approach [3.085995273374333]
  Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous process conditioned on the realization of a random intensity function. Existing implementations of doubly-stochastic spatial models are computationally demanding, often have limited theoretical guarantee, and/or rely on restrictive assumptions.
  arXiv  Detail & Related papers  (2023-06-11T19:48:39Z)
• Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence [65.63201894457404]
  We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear differential equations.<n>The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations.
  arXiv  Detail & Related papers  (2023-05-24T20:43:47Z)
• The Implicit Delta Method [61.36121543728134]
  In this paper, we propose an alternative, the implicit delta method, which works by infinitesimally regularizing the training loss of uncertainty. We show that the change in the evaluation due to regularization is consistent for the variance of the evaluation estimator, even when the infinitesimal change is approximated by a finite difference.
  arXiv  Detail & Related papers  (2022-11-11T19:34:17Z)
• Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
  We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing. We study the case where probability distributions are not known a priori but need to be estimated from data.
  arXiv  Detail & Related papers  (2022-08-29T16:16:22Z)
• Uncertainty Quantification for Traffic Forecasting: A Unified Approach [21.556559649467328]
  Uncertainty is an essential consideration for time series forecasting tasks. In this work, we focus on quantifying the uncertainty of traffic forecasting. We develop Deep S-Temporal Uncertainty Quantification (STUQ), which can estimate both aleatoric and relational uncertainty.
  arXiv  Detail & Related papers  (2022-08-11T15:21:53Z)
• Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints [0.0]
  We present a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a boundary value problem from a prior probability model. A statistical surrogate model of the implicit mapping, which represents the constraints, is introduced. In a second part, an application is presented to illustrate the proposed theory and is also, as such, a contribution to the three-dimensional homogenization of heterogeneous linear elastic media.
  arXiv  Detail & Related papers  (2022-02-10T16:00:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.