Locally Differentially Private Reinforcement Learning for Linear Mixture Markov Decision Processes

Chonghua Liao, Jiafan He, Quanquan Gu
Proceedings of The 14th Asian Conference on Machine Learning, PMLR 189:627-642, 2023.

Abstract

Reinforcement learning (RL) algorithms can be used to provide personalized services, which rely on users’ private and sensitive data. To protect the users’ privacy, privacy-preserving RL algorithms are in demand. In this paper, we study RL with linear function approximation and local differential privacy (LDP) guarantees. We propose a novel $(\varepsilon, \delta)$-LDP algorithm for learning a class of Markov decision processes (MDPs) dubbed linear mixture MDPs, and obtains an $\tilde{\mathcal{O}}( d^{5/4}H^{7/4}T^{3/4}\left(\log(1/\delta)\right)^{1/4}\sqrt{1/\varepsilon})$ regret, where $d$ is the dimension of feature mapping, $H$ is the length of the planning horizon, and $T$ is the number of interactions with the environment. We also prove a lower bound $\Omega(dH\sqrt{T}/\left(e^{\varepsilon}(e^{\varepsilon}-1)\right))$ for learning linear mixture MDPs under $\varepsilon$-LDP constraint. Experiments on synthetic datasets verify the effectiveness of our algorithm. To the best of our knowledge, this is the first provable privacy-preserving RL algorithm with linear function approximation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v189-liao23a, title = {Locally Differentially Private Reinforcement Learning for Linear Mixture Markov Decision Processes}, author = {Liao, Chonghua and He, Jiafan and Gu, Quanquan}, booktitle = {Proceedings of The 14th Asian Conference on Machine Learning}, pages = {627--642}, year = {2023}, editor = {Khan, Emtiyaz and Gonen, Mehmet}, volume = {189}, series = {Proceedings of Machine Learning Research}, month = {12--14 Dec}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v189/liao23a/liao23a.pdf}, url = {https://proceedings.mlr.press/v189/liao23a.html}, abstract = {Reinforcement learning (RL) algorithms can be used to provide personalized services, which rely on users’ private and sensitive data. To protect the users’ privacy, privacy-preserving RL algorithms are in demand. In this paper, we study RL with linear function approximation and local differential privacy (LDP) guarantees. We propose a novel $(\varepsilon, \delta)$-LDP algorithm for learning a class of Markov decision processes (MDPs) dubbed linear mixture MDPs, and obtains an $\tilde{\mathcal{O}}( d^{5/4}H^{7/4}T^{3/4}\left(\log(1/\delta)\right)^{1/4}\sqrt{1/\varepsilon})$ regret, where $d$ is the dimension of feature mapping, $H$ is the length of the planning horizon, and $T$ is the number of interactions with the environment. We also prove a lower bound $\Omega(dH\sqrt{T}/\left(e^{\varepsilon}(e^{\varepsilon}-1)\right))$ for learning linear mixture MDPs under $\varepsilon$-LDP constraint. Experiments on synthetic datasets verify the effectiveness of our algorithm. To the best of our knowledge, this is the first provable privacy-preserving RL algorithm with linear function approximation.} }
Endnote
%0 Conference Paper %T Locally Differentially Private Reinforcement Learning for Linear Mixture Markov Decision Processes %A Chonghua Liao %A Jiafan He %A Quanquan Gu %B Proceedings of The 14th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Emtiyaz Khan %E Mehmet Gonen %F pmlr-v189-liao23a %I PMLR %P 627--642 %U https://proceedings.mlr.press/v189/liao23a.html %V 189 %X Reinforcement learning (RL) algorithms can be used to provide personalized services, which rely on users’ private and sensitive data. To protect the users’ privacy, privacy-preserving RL algorithms are in demand. In this paper, we study RL with linear function approximation and local differential privacy (LDP) guarantees. We propose a novel $(\varepsilon, \delta)$-LDP algorithm for learning a class of Markov decision processes (MDPs) dubbed linear mixture MDPs, and obtains an $\tilde{\mathcal{O}}( d^{5/4}H^{7/4}T^{3/4}\left(\log(1/\delta)\right)^{1/4}\sqrt{1/\varepsilon})$ regret, where $d$ is the dimension of feature mapping, $H$ is the length of the planning horizon, and $T$ is the number of interactions with the environment. We also prove a lower bound $\Omega(dH\sqrt{T}/\left(e^{\varepsilon}(e^{\varepsilon}-1)\right))$ for learning linear mixture MDPs under $\varepsilon$-LDP constraint. Experiments on synthetic datasets verify the effectiveness of our algorithm. To the best of our knowledge, this is the first provable privacy-preserving RL algorithm with linear function approximation.
APA
Liao, C., He, J. & Gu, Q.. (2023). Locally Differentially Private Reinforcement Learning for Linear Mixture Markov Decision Processes. Proceedings of The 14th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 189:627-642 Available from https://proceedings.mlr.press/v189/liao23a.html.

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