Federated Bayesian Optimization via Thompson Sampling

TL;DR

This paper introduces federated Thompson sampling, a novel approach combining Bayesian optimization and federated learning to efficiently optimize black-box functions across distributed, privacy-sensitive edge devices.

Contribution

It develops a federated BO method using Thompson sampling and Fourier features, with theoretical convergence guarantees for heterogeneous agents.

Findings

Reduces communication overhead in federated BO.

Demonstrates improved efficiency and performance in experiments.

Provides theoretical convergence guarantees for heterogeneous settings.

Abstract

Bayesian optimization (BO) is a prominent approach to optimizing expensive-to-evaluate black-box functions. The massive computational capability of edge devices such as mobile phones, coupled with privacy concerns, has led to a surging interest in federated learning (FL) which focuses on collaborative training of deep neural networks (DNNs) via first-order optimization techniques. However, some common machine learning tasks such as hyperparameter tuning of DNNs lack access to gradients and thus require zeroth-order/black-box optimization. This hints at the possibility of extending BO to the FL setting (FBO) for agents to collaborate in these black-box optimization tasks. This paper presents federated Thompson sampling (FTS) which overcomes a number of key challenges of FBO and FL in a principled way: We (a) use random Fourier features to approximate the Gaussian process surrogate model used in BO, which naturally produces the parameters to be exchanged between agents, (b) design FTS based on Thompson sampling, which significantly reduces the number of parameters to be exchanged, and (c) provide a theoretical convergence guarantee that is robust against heterogeneous agents, which is a major challenge in FL and FBO. We empirically demonstrate the effectiveness of FTS in terms of communication efficiency, computational efficiency, and practical performance.