Federated X-Armed Bandit

TL;DR

This paper introduces Fed-PNE, a federated algorithm for heterogeneous X-armed bandit problems that achieves sublinear regret, preserves privacy with minimal communication, and outperforms existing methods on synthetic and real data.

Contribution

It is the first to propose a federated framework for X-armed bandits and develops a novel algorithm leveraging topological structure and weak smoothness.

Findings

Achieves sublinear cumulative regret in federated X-armed bandits.

Requires only logarithmic communication, ensuring privacy.

Outperforms baseline algorithms on synthetic and real datasets.

Abstract

This work establishes the first framework of federated $\mathcal{X}$-armed bandit, where different clients face heterogeneous local objective functions defined on the same domain and are required to collaboratively figure out the global optimum. We propose the first federated algorithm for such problems, named \texttt{Fed-PNE}. By utilizing the topological structure of the global objective inside the hierarchical partitioning and the weak smoothness property, our algorithm achieves sublinear cumulative regret with respect to both the number of clients and the evaluation budget. Meanwhile, it only requires logarithmic communications between the central server and clients, protecting the client privacy. Experimental results on synthetic functions and real datasets validate the advantages of \texttt{Fed-PNE} over various centralized and federated baseline algorithms.