Gradient-based federated Bayesian optimization

Bayesian optimization (BO) has evolved from traditional single-agent optimization to multi-agent collaborative optimization, known as federated BO, aiming to solve global optimization tasks such as federated hyperparameter tuning. Existing research on federated BO shares weight vectors sampled from Gaussian processes, approximated using random Fourier features, with a server for information aggregation. This line of approach helps protect the privacy of agents but may limit the performance of the algorithm. Unlike existing federated BO approaches, we propose to cluster each agent according to its characteristics, and transmit the gradients of acquisition functions between the server and agents for information aggregation. This allows for a more accurate representation of the overall landscape of the global acquisition function without explicitly constructing it. Moreover, we design a two-stage mechanism to infill the next query input based on the aggregated gradients. Specifically, multiple promising solutions are first suggested based on the aggregated gradients. Then, each agent further selects the one with the best local acquisition function value as the newly infilled solution for real function evaluation. The resulting gradient-based federated BO, termed FGBO, has demonstrated to be very competitive in tackling a set of benchmark functions and real-world problems in a privacy-preserving way.