Description
"Active Learning of Conditional Mean Embeddings via Bayesian Optimisation
Sayak Ray Chowdhury (Indian Institute of Science)*; Rafael Oliveira (The University of Sydney); Fabio Ramos (NVIDIA, The University of Sydney)
We consider the problem of sequentially optimising the conditional expectation of an objective function, with both the conditional distribution and the objective function assumed to be fixed but unknown. Assuming that the objective function belongs to a reproducing kernel Hilbert space (RKHS), we provide a novel upper confidence bound (UCB) based algorithm CME-UCB via estimation of the conditional mean embeddings (CME), and derive its regret bound. Along the way, we derive novel approximation guarantees for the CME estimates. Finally, experiments are carried out in a synthetic example and in a likelihood-free inference application that highlight the useful insights of the proposed method."