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A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning
Eloïse Berthier · Ziad Kobeissi · Francis Bach


Temporal-difference learning is a popular algorithm for policy evaluation. In this paper, we study the convergence of the regularized non-parametric TD(0) algorithm, in both the independent and Markovian observation settings. In particular, when TD is performed in a universal reproducing kernel Hilbert space (RKHS), we prove convergence of the averaged iterates to the optimal value function, even when it does not belong to the RKHS. We provide explicit convergence rates that depend on a source condition relating the regularity of the optimal value function to the RKHS. We illustrate this convergence numerically on a simple continuous-state Markov reward process.

Author Information

Eloïse Berthier (Inria / ENS Paris)
Ziad Kobeissi (INRIA)
Francis Bach (INRIA - Ecole Normale Superieure)

Francis Bach is a researcher at INRIA, leading since 2011 the SIERRA project-team, which is part of the Computer Science Department at Ecole Normale Supérieure in Paris, France. After completing his Ph.D. in Computer Science at U.C. Berkeley, he spent two years at Ecole des Mines, and joined INRIA and Ecole Normale Supérieure in 2007. He is interested in statistical machine learning, and especially in convex optimization, combinatorial optimization, sparse methods, kernel-based learning, vision and signal processing. He gave numerous courses on optimization in the last few years in summer schools. He has been program co-chair for the International Conference on Machine Learning in 2015.

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