Federated Linear Contextual Bandits with User-level Differential Privacy
This addresses privacy-preserving sequential decision-making in federated systems, which is incremental as it extends existing bandit and DP work to user-level privacy.
The paper tackles federated linear contextual bandits with user-level differential privacy, introducing a framework and analyzing trade-offs between learning regrets and privacy guarantees. For central DP, they propose a near-optimal algorithm with matching bounds, while for local DP, they derive lower bounds showing regret blow-up factors like min{1/ε, M}.
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 $(\varepsilon,δ)$-LDP must suffer a regret blow-up factor at least $\min\{1/\varepsilon,M\}$ or $\min\{1/\sqrt{\varepsilon},\sqrt{M}\}$ under different conditions.