(Private) Kernelized Bandits with Distributed Biased Feedback

TL;DR

This paper introduces a distributed kernelized bandit algorithm that effectively manages biased feedback from a subset of users, reducing communication and computation costs while providing privacy guarantees and achieving sublinear regret.

Contribution

The paper proposes the DPBE algorithm for distributed kernelized bandits with biased feedback, incorporating privacy models and demonstrating improved efficiency and theoretical regret bounds.

Findings

Achieves sublinear regret of  O(T^{1-rac{eta}{2}} + \u221A{rac{ ext{gamma}_T T}{}})

Reduces communication and computation costs compared to existing algorithms

Provides privacy guarantees under various differential privacy models

Abstract

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 the action chosen by a central entity, but it is difficult to collect feedback from all users. Instead, only biased feedback (due to user heterogeneity) from a subset of users may be available. In addition to such partial biased feedback, we are also faced with two practical challenges due to communication cost and computation complexity. To tackle these challenges, we carefully design a new \emph{distributed phase-then-batch-based elimination (\texttt{DPBE})} algorithm, which samples users in phases for collecting feedback to reduce the bias and employs \emph{maximum variance reduction} to select actions in batches within each phase. By properly choosing the phase length, the batch size, and the confidence width used for eliminating suboptimal actions, we show that \texttt{DPBE} achieves a sublinear regret of $\tilde{O}(T^{1-\alpha/2}+\sqrt{\gamma_T T})$, where $\alpha\in (0,1)$ is the user-sampling parameter one can tune. Moreover, \texttt{DPBE} can significantly reduce both communication cost and computation complexity in distributed kernelized bandits, compared to some variants of the state-of-the-art algorithms (originally developed for standard kernelized bandits). Furthermore, by incorporating various \emph{differential privacy} models (including the central, local, and shuffle models), we generalize \texttt{DPBE} to provide privacy guarantees for users participating in the distributed learning process. Finally, we conduct extensive simulations to validate our theoretical results and evaluate the empirical performance.