English

Finite time analysis of temporal difference learning with linear function approximation: Tail averaging and regularisation

Machine Learning 2024-09-20 v3 Artificial Intelligence Systems and Control Systems and Control Machine Learning

Abstract

We study the finite-time behaviour of the popular temporal difference (TD) learning algorithm when combined with tail-averaging. We derive finite time bounds on the parameter error of the tail-averaged TD iterate under a step-size choice that does not require information about the eigenvalues of the matrix underlying the projected TD fixed point. Our analysis shows that tail-averaged TD converges at the optimal O(1/t)O\left(1/t\right) rate, both in expectation and with high probability. In addition, our bounds exhibit a sharper rate of decay for the initial error (bias), which is an improvement over averaging all iterates. We also propose and analyse a variant of TD that incorporates regularisation. From analysis, we conclude that the regularised version of TD is useful for problems with ill-conditioned features.

Keywords

Cite

@article{arxiv.2210.05918,
  title  = {Finite time analysis of temporal difference learning with linear function approximation: Tail averaging and regularisation},
  author = {Gandharv Patil and Prashanth L. A. and Dheeraj Nagaraj and Doina Precup},
  journal= {arXiv preprint arXiv:2210.05918},
  year   = {2024}
}
R2 v1 2026-06-28T03:23:55.209Z