A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning

Eloïse Berthier; Ziad Kobeissi; Francis Bach

A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning

Eloïse Berthier, Ziad Kobeissi, Francis Bach

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
Editors	S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh
Publisher	Neural information processing systems foundation
ISBN (Electronic)	9781713871088
Publication status	Published - 1 Jan 2022
Event	36th Conference on Neural Information Processing Systems, NeurIPS 2022 - New Orleans, United States Duration: 28 Nov 2022 → 9 Dec 2022

Publication series

Name	Advances in Neural Information Processing Systems
Volume	35
ISSN (Print)	1049-5258

Conference

Conference	36th Conference on Neural Information Processing Systems, NeurIPS 2022
Country/Territory	United States
City	New Orleans
Period	28/11/22 → 9/12/22

Cite this

Berthier, E., Kobeissi, Z., & Bach, F. (2022). A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, & A. Oh (Eds.), Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022 (Advances in Neural Information Processing Systems; Vol. 35). Neural information processing systems foundation.

Berthier, Eloïse ; Kobeissi, Ziad ; Bach, Francis. / A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning. Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. editor / S. Koyejo ; S. Mohamed ; A. Agarwal ; D. Belgrave ; K. Cho ; A. Oh. Neural information processing systems foundation, 2022. (Advances in Neural Information Processing Systems).

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title = "A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning",

abstract = "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 = "Elo{\"i}se Berthier and Ziad Kobeissi and Francis Bach",

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Berthier, E, Kobeissi, Z & Bach, F 2022, A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning. in S Koyejo, S Mohamed, A Agarwal, D Belgrave, K Cho & A Oh (eds), Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. Advances in Neural Information Processing Systems, vol. 35, Neural information processing systems foundation, 36th Conference on Neural Information Processing Systems, NeurIPS 2022, New Orleans, United States, 28/11/22.

A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning. / Berthier, Eloïse; Kobeissi, Ziad; Bach, Francis.
Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. ed. / S. Koyejo; S. Mohamed; A. Agarwal; D. Belgrave; K. Cho; A. Oh. Neural information processing systems foundation, 2022. (Advances in Neural Information Processing Systems; Vol. 35).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Kobeissi, Ziad

AU - Bach, Francis

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Y1 - 2022/1/1

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:85163190605

T3 - Advances in Neural Information Processing Systems

BT - Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022

A2 - Koyejo, S.

A2 - Mohamed, S.

A2 - Agarwal, A.

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A2 - Cho, K.

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Berthier E, Kobeissi Z, Bach F. A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning. In Koyejo S, Mohamed S, Agarwal A, Belgrave D, Cho K, Oh A, editors, Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022. Neural information processing systems foundation. 2022. (Advances in Neural Information Processing Systems).

A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning

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