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.

Predicting booking probability and value at the traveler level plays a central role in computational advertising for massive two-sided vacation rental marketplaces. These marketplaces host millions of travelers with long shopping cycles, spending a lot of time in the discovery phase. The footprint of the travelers in their discovery is a useful data source to help these marketplaces to predict shopping probability and value. However, there is no one-size-fits-all solution for this purpose. In this paper, we propose a hybrid model that infuses deep and shallow neural network embeddings into a gradient boosting tree model. This approach allows the latent preferences of millions of travelers to be automatically learned from sparse session logs. In addition, we present the architecture that we deployed into our production system. We find that there is a pragmatic sweet spot between expensive complex deep neural networks and simple shallow neural networks that can increase the prediction performance of a model by seven percent, based on offline analysis.