Compared to global BO methods, locally searching in the latent space can be more efficient since it can avoid over-exploration of areas that are unreliable. The trust region Bayesian optimiza-tion (TURBO) algorithm, which is at the heart of the Local latent space Bayesian optimization (LOLBO) algorithm, can use hyper-rectangular zones (trust regions) that are iteratively shrinking to narrow down the search areas and get closer to the optimal data points. As an advancement, LOLBO can navigate the latent space by jointly training the VAE with the surrogate model after multiple failed optimization attempts, enabling more effective exploration of better molecules.