Differentially Private Linear Bandits with Partial Distributed Feedback

TL;DR

This paper introduces a differentially private distributed linear bandit algorithm, DP-DPE, that efficiently learns global rewards with partial feedback while ensuring privacy, achieving sublinear regret and communication costs.

Contribution

The paper proposes DP-DPE, a unified framework for differentially private distributed linear bandits that balances privacy, regret, and communication efficiency, with privacy guarantees achieved at minimal additional cost.

Findings

DP-DPE achieves sublinear regret and communication cost.

Privacy guarantees are obtained 'for free' as an additive cost.

Simulations confirm theoretical advantages of DP-DPE.

Abstract

In this paper, we study the problem of global reward maximization with only partial distributed feedback. This problem is motivated by several real-world applications (e.g., cellular network configuration, dynamic pricing, and policy selection) where an action taken by a central entity influences a large population that contributes to the global reward. However, collecting such reward feedback from the entire population not only incurs a prohibitively high cost but often leads to privacy concerns. To tackle this problem, we consider differentially private distributed linear bandits, where only a subset of users from the population are selected (called clients) to participate in the learning process and the central server learns the global model from such partial feedback by iteratively aggregating these clients' local feedback in a differentially private fashion. We then propose a unified algorithmic learning framework, called differentially private distributed phased elimination (DP-DPE), which can be naturally integrated with popular differential privacy (DP) models (including central DP, local DP, and shuffle DP). Furthermore, we prove that DP-DPE achieves both sublinear regret and sublinear communication cost. Interestingly, DP-DPE also achieves privacy protection ``for free'' in the sense that the additional cost due to privacy guarantees is a lower-order additive term. In addition, as a by-product of our techniques, the same results of ``free" privacy can also be achieved for the standard differentially private linear bandits. Finally, we conduct simulations to corroborate our theoretical results and demonstrate the effectiveness of DP-DPE.