Analysis of a Target-Based Actor-Critic Algorithm with Linear Function Approximation

Anas Barakat, Pascal Bianchi, Julien Lehmann
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:991-1040, 2022.

Abstract

Actor-critic methods integrating target networks have exhibited a stupendous empirical success in deep reinforcement learning. However, a theoretical understanding of the use of target networks in actor-critic methods is largely missing in the literature. In this paper, we reduce this gap between theory and practice by proposing the first theoretical analysis of an online target-based actor-critic algorithm with linear function approximation in the discounted reward setting. Our algorithm uses three different timescales: one for the actor and two for the critic. Instead of using the standard single timescale temporal difference (TD) learning algorithm as a critic, we use a two timescales target-based version of TD learning closely inspired from practical actor-critic algorithms implementing target networks. First, we establish asymptotic convergence results for both the critic and the actor under Markovian sampling. Then, we provide a finite-time analysis showing the impact of incorporating a target network into actor-critic methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-barakat22a, title = { Analysis of a Target-Based Actor-Critic Algorithm with Linear Function Approximation }, author = {Barakat, Anas and Bianchi, Pascal and Lehmann, Julien}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {991--1040}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/barakat22a/barakat22a.pdf}, url = {https://proceedings.mlr.press/v151/barakat22a.html}, abstract = { Actor-critic methods integrating target networks have exhibited a stupendous empirical success in deep reinforcement learning. However, a theoretical understanding of the use of target networks in actor-critic methods is largely missing in the literature. In this paper, we reduce this gap between theory and practice by proposing the first theoretical analysis of an online target-based actor-critic algorithm with linear function approximation in the discounted reward setting. Our algorithm uses three different timescales: one for the actor and two for the critic. Instead of using the standard single timescale temporal difference (TD) learning algorithm as a critic, we use a two timescales target-based version of TD learning closely inspired from practical actor-critic algorithms implementing target networks. First, we establish asymptotic convergence results for both the critic and the actor under Markovian sampling. Then, we provide a finite-time analysis showing the impact of incorporating a target network into actor-critic methods. } }
Endnote
%0 Conference Paper %T Analysis of a Target-Based Actor-Critic Algorithm with Linear Function Approximation %A Anas Barakat %A Pascal Bianchi %A Julien Lehmann %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-barakat22a %I PMLR %P 991--1040 %U https://proceedings.mlr.press/v151/barakat22a.html %V 151 %X Actor-critic methods integrating target networks have exhibited a stupendous empirical success in deep reinforcement learning. However, a theoretical understanding of the use of target networks in actor-critic methods is largely missing in the literature. In this paper, we reduce this gap between theory and practice by proposing the first theoretical analysis of an online target-based actor-critic algorithm with linear function approximation in the discounted reward setting. Our algorithm uses three different timescales: one for the actor and two for the critic. Instead of using the standard single timescale temporal difference (TD) learning algorithm as a critic, we use a two timescales target-based version of TD learning closely inspired from practical actor-critic algorithms implementing target networks. First, we establish asymptotic convergence results for both the critic and the actor under Markovian sampling. Then, we provide a finite-time analysis showing the impact of incorporating a target network into actor-critic methods.
APA
Barakat, A., Bianchi, P. & Lehmann, J.. (2022). Analysis of a Target-Based Actor-Critic Algorithm with Linear Function Approximation . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:991-1040 Available from https://proceedings.mlr.press/v151/barakat22a.html.

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