Adaptive Control of Differentially Private Linear Quadratic Systems

Abstract

In this paper we study the problem of regret minimization in reinforcement learning (RL) under differential privacy constraints. This work is motivated by the wide range of RL applications for providing personalized service, where privacy concerns are becoming paramount. In contrast to previous works, we take the first step towards non-tabular RL settings, while providing a rigorous privacy guarantee. In particular, we consider the adaptive control of differentially private linear quadratic (LQ) systems. We develop the first private RL algorithm, Private-OFU-RL which is able to attain a sub-linear regret while guaranteeing privacy protection. More importantly, the additional cost due to privacy is only on the order of \\fracłn(1/δ)1/4\\varepsilon1/2 given privacy parameters \\varepsilon, δ > 0. Through this process, we also provide a general procedure for adaptive control of LQ systems under changing regularizers, which not only generalizes previous non-private controls, but also serves as the basis for general private controls. © 2021 IEEE., keywords=Control theory; Information theory; Privacy by design; Reinforcement learning, Adaptive Control; Additional costs; Differential privacies; Linear quadratic; Personalized service; Privacy concerns; Privacy protection; Regret minimization, Adaptive control systems, fundingdetails1=National Science FoundationNational Science Foundation, NSF, CNS-1901057, CNS-2007231, fundingdetails2=Office of Naval ResearchOffice of Naval Research, ONR, N00014-17-1-241, fundingtext1=However, in most practical scenarios, the feedback from the users often encodes their sensitive information. For example, in a personalized healthcare setting, the states of a patient include personal information such as age, gender, height, weight, state of the treatment etc. Similarly, the states of a virtual keyboard user (e.g., â��Equal contribution. This work was funded in part through NSF grants: CNS-1901057 and CNS-2007231, and an Office of Naval Research under Grant N00014-17-1-241 Google GBoard users) are the words and sentences she typed in, which inevitably contain private information about the user. Another intriguing example is the social robot for second language education of children. The states include facial expressions, and the rewards contain whether they have passed the quiz. Users may not want any of this information to be inferred by others. This directly results in an increasing concern about privacy protection in personalized services. To be more specific, although a user might be willing to share her own information to the agent to obtain a better tailored service, she would not like to allow third parties to infer her private information from the output of the learning algorithm. For example, in the healthcare application, we would like to ensure that an adversary with arbitrary side knowledge cannot infer a particular patientâ��s state from the treatments prescribed to her., references=1. Li, L., Chu, W., Langford, J., Schapire, R.E., A contextualbandit approach to personalized news article recommendation (2010) Proceedings of the 19th International Conference on World Wide Web, pp. 661-670; 2. Zhao, Y., Kosorok, M.R., Zeng, D., Reinforcement learning design for cancer clinical trials (2009) Statistics in Medicine, 28 (26), pp. 3294-3315; 3. Sharma, A.R., Kaushik, P., Literature survey of statistical, deep and reinforcement learning in natural language processing (2017) 2017 International Conference on Computing, Communication and Automation (ICCCA, pp. 350-354; 4. Gordon, G., Spaulding, S., Westlund, J.K., Lee, J.J., Plummer, L., Martinez, M., Das, M., Breazeal, C., Affective personalization of a social robot tutor for children's second language skills (2016) Proceedings of the Aaai Conference on Artificial Intelligence, 30 (1); 5. Dwork, C., Differential privacy: A survey of results (2008) International Conference on Theory and Applications of Models of Computation, pp. 1-19. , Sprin