Federated Linear Contextual Bandits with User-level Differential Privacy

TL;DR

This paper introduces a unified framework for federated linear contextual bandits with user-level differential privacy, analyzing the trade-offs between privacy guarantees and learning regret, and proposing near-optimal algorithms.

Contribution

It formalizes user-level DP in federated bandits, proposes the $ exttt{ROBIN}$ algorithm for central DP, and establishes fundamental regret bounds under both central and local DP.

Findings

ROBIN algorithm is near-optimal for user-level CDP.

Lower bounds show regret blow-up under user-level LDP.

Trade-offs between privacy parameters and regret are characterized.

Abstract

This paper studies federated linear contextual bandits under the notion of user-level differential privacy (DP). We first introduce a unified federated bandits framework that can accommodate various definitions of DP in the sequential decision-making setting. We then formally introduce user-level central DP (CDP) and local DP (LDP) in the federated bandits framework, and investigate the fundamental trade-offs between the learning regrets and the corresponding DP guarantees in a federated linear contextual bandits model. For CDP, we propose a federated algorithm termed as $\texttt{ROBIN}$ and show that it is near-optimal in terms of the number of clients $M$ and the privacy budget $\varepsilon$ by deriving nearly-matching upper and lower regret bounds when user-level DP is satisfied. For LDP, we obtain several lower bounds, indicating that learning under user-level $(\varepsilon,\delta)$-LDP must suffer a regret blow-up factor at least $\min\{1/\varepsilon,M\}$ or $\min\{1/\sqrt{\varepsilon},\sqrt{M}\}$ under different conditions.