2022/02/02 by Dung Daniel Ngo, Ngo, Dung Daniel, Giuseppe Vietri +3
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Age of Information Optimization #FOS: Computer and information sciences #Machine Learning (cs.LG) #Privacy-Preserving Technologies in Data
paper · pdf · doi:10.48550/arxiv.2202.01292
openalex publication_date 2022/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study privacy-preserving exploration in sequential decision-making for environments that rely on sensitive data such as medical records. In particular, we focus on solving the problem of reinforcement learning (RL) subject to the constraint of (joint) differential privacy in the linear MDP setting, where both dynamics and rewards are given by linear functions. Prior work on this problem due to Luyo et al. (2021) achieves a regret rate that has a dependence of O(K3/5) on the number of episodes K. We provide a private algorithm with an improved regret rate with an optimal dependence of O(√(K)) on the number of episodes. The key recipe for our stronger regret guarantee is the adaptivity in the policy update schedule, in which an update only occurs when sufficient changes in the data are detected. As a result, our algorithm benefits from low switching cost and only performs O(log(K)) updates, which greatly reduces the amount of privacy noise. Finally, in the most prevalent privacy regimes where the privacy parameter ε is a constant, our algorithm incurs negligible privacy cost -- in comparison with the existing non-private regret bounds, the additional regret due to privacy appears in lower-order terms.