Extending Bayesian optimization to batch evaluation can enable the designer to make the most use of parallel computing technology. Most of current batch approaches use artificial functions to simulate the sequential Bayesian optimization algorithm's behavior to select a batch of points for parallel evaluation. However, as the batch size grows, the accumulated error introduced by these artificial functions increases rapidly, which dramatically decreases the optimization efficiency of the algorithm. In this work, we propose a simple and efficient approach to extend Bayesian optimization to batch evaluation. Different from existing batch approaches, the idea of the new approach is to draw a batch of subspaces of the original problem and select one acquisition point from each subspace. To achieve this, we propose the expected subspace improvement criterion to measure the amount of the improvement that a candidate point can achieve within a certain subspace. By optimizing these expected subspace improvement functions simultaneously, we can get a batch of query points for expensive evaluation. Numerical experiments show that our proposed approach can achieve near-linear speedup when compared with the sequential Bayesian optimization algorithm, and performs very competitively when compared with eight state-of-the-art batch algorithms. This work provides a simple yet efficient approach for batch Bayesian optimization. A Matlab implementation of our approach is available at https://github.com/zhandawei/Expected_Subspace_Improvement_Batch_Bayesian_Optimization

Traditional online maps, widely used on Internet such as Google map and Baidu map, are rendered from vector data. Timely updating online maps from vector data, of which the generating is time-consuming, is a difficult mission. It is a shortcut to generate online maps in time from remote sensing images, which can be acquired timely without vector data. However, this mission used to be challenging or even impossible. Inspired by image-to-image translation (img2img) techniques based on generative adversarial network (GAN), we propose a semi-supervised structure-augmented online map GAN (S$^{2}$OMGAN) model to generate online maps directly from remote sensing images. In this model, we designed a semi-supervised learning strategy to pre-train S$^{2}$OMGAN on rich unpaired samples and finetune it on limited paired samples in reality. We also designed image gradient L1 loss and image gradient structure loss to generate an online map with global topological relationship and detailed edge curves of objects, which are important in cartography. Moreover, we propose edge structural similarity index (ESSI) as a metric to evaluate the quality of topological consistency between generated online maps and ground truths. Experimental results present that S$^{2}$OMGAN outperforms state-of-the-art (SOTA) works according to mean squared error, structural similarity index and ESSI. Also, S$^{2}$OMGAN wins more approval than SOTA in the human perceptual test on visual realism of cartography. Our work shows that S$^{2}$OMGAN is potentially a new paradigm to produce online maps. Our implementation of the S$^{2}$OMGAN is available at \url{https://github.com/imcsq/S2OMGAN}.