Federated X-Armed Bandit
This work addresses collaborative optimization in federated learning settings, offering a novel framework for privacy-preserving decision-making across distributed clients.
The paper tackles the problem of federated X-armed bandits with heterogeneous local objectives, proposing the Fed-PNE algorithm that achieves sublinear cumulative regret with respect to clients and budget while requiring only logarithmic communications.
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.