Federated Linear Contextual Bandits with User-level Differential Privacy

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 ROBIN and show that it is near-optimal in terms of the number of clients M and the privacy budget ε 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 (ε, δ)-LDP must suffer a regret blow-up factor at least min{1/ε, M} or min{1/^√ε, ^√M} under different conditions.