(Private) Kernelized Bandits with Distributed Biased Feedback

In this paper, we study kernelized bandits with distributed biased feedback. This problem is motivated by several real-world applications (such as dynamic pricing, cellular network configuration, and policy making), where users from a large population contribute to the reward of action chosen central entity, but it difficult collect feedback all users. Instead, only (due user heterogeneity) subset may be available. addition such partial feedback, are also faced two practical challenges due communication cost computation complexity. To tackle these challenges, carefully design new phase-then-batch-based elimination (DPBE) algorithm, which samples in phases for collecting reduce bias employs maximum variance reduction select actions batches within each phase. By properly choosing phase length, batch size, confidence width used eliminating suboptimal actions, show that DPBE achieves sublinear regret ~O(T1-α/2 +√γT T), α ∈ (0,1) user-sampling parameter one can tune. Moreover, significantly both complexity bandits, compared some variants state-of-the-art algorithms (originally developed standard bandits). Furthermore, incorporating various differential privacy models (including central, local, shuffle models), generalize provide guarantees participating learning process. Finally, conduct extensive simulations validate our theoretical results evaluate empirical performance.