Fast and Robust Convergence Rate for TD(0) with Linear Function Approximation, Universal Learning Steps and I.I.D. Samples

Title:Fast and Robust Convergence Rate for TD(0) with Linear Function Approximation, Universal Learning Steps and I.I.D. Samples

Abstract:In this paper, we study the finite-time behavior of the TD(0) temporal-difference method with linear function approximation (LFA). We consider on-policy independent and identically distributed (i.i.d.) samples, a constant learning step, and the Polyak-Juditsky averaging method. We establish a new convergence rate, for the Mean-Square Error (MSE) on the approximated function, that is (i) fast in the sense that it admits an optimal dependency in the number of iterations k (i.e., of order 1/k), (ii) robust to ill-conditioning: it only depends on an initial error and modelindependent constants and (iii) sharp up to a multiplicative constant lower than 11. In particular, it does not depend on the smallest eigenvalue of the uncentered covariance matrix of the linear parametrization, unlike all pre-existing O(1/k) rates in the TD(0) literature. We also introduce PCTD(0), a variant of TD(0), which benefits from better convergence properties under an additional assumption of strong mixing on the Markov Chain.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2606.05967 [stat.ML]

(or arXiv:2606.05967v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2606.05967 Focus to learn more arXiv-issued DOI via DataCite

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