The decoder autoregressively generates the target sequence based on the encoded representation.
When a property element's content is string literal, it may be possible to use it as an XML attribute on the containing node element. This can be done for multiple properties on the same node element only if the property element name is not repeated (required by XML — attribute names are unique on an XML element) and any in-scope xml:lang on the property element's string literal (if any) are the same (see Section 2.7) This abbreviation is known as a Property Attribute and can be applied to any node element.
While Bayesian optimization is applied in many fields, its utilization remains low due to its high optimization cost. To mitigate the dilemma, the works [50,51,52] have also been proposed for transfer learning and meta learning in Bayesian optimization; however, these methods are limited to transferring knowledge among functions that share the same domain. Similarly, Wang et al. [53] demonstrated that pre-training enhances the acquisition of a more effective Gaussian process prior, leading to improved Bayesian optimization performance across various functions within the same domain. Nevertheless, the main challenge in the above methods lies in how to perform data selection for different tasks. BO can leverage prior knowledge about the expected behavior of the objective function’s structure. For instance, the work in [54] proposed structural priors customized for high-dimensional problems, tackling the problem of excessive exploration along the boundaries. Siivola et al. [55] introduced indicators at the boundaries of the search space to guide Bayesian optimization towards the center. All of above-mentioned methods merge the prior information about specific properties of the function space. Nonetheless, they usually do not guide the acquisition function to search towards specific regions in the search space, resulting in limited influence for the user over the choice of points to assess. In some situations, users evidently specify a prior that encapsulates their beliefs about the probable location of the optimum [8]. BOPrO [39] combined the user-provided prior distribution to partition the function space based on the TPE surrogate model. However, it does not provide theoretical guarantees for the algorithm. Ramachandran et al. [56] leveraged the probability integral transform to deform the search space, expanding areas with high probability and contracting others. 𝜋
BO [41] allowed users to define their expectation about the optimum of objective function; nonetheless, it has not generalized to other acquisition functions.
3. Preliminaries
We review a brief background of the mainstream surrogate model GP and some of the existing acquisition functions from the BO literature in this section, and then depict the problem setting in our paper. The key notations, which are important for the PMCBO method, are summarized in Table 2.
The language is widely used in web development, data analysis, artificial intelligence, scientific computing, and automation. Its extensive standard library and large ecosystem of third-party packages, such as NumPy, pandas, and TensorFlow, make it a preferred choice for many developers and researchers.
Python is dynamically typed and garbage-collected. It features a comprehensive standard library that supports many common programming tasks. The language design philosophy is summarized in The Zen of Python, which includes principles such as "Beautiful is better than ugly" and "Simple is better than complex."
Major implementations include CPython, the reference implementation written in C, as well as alternative implementations like PyPy, Jython, and IronPython. Python 3, the current major version, introduced several improvements over Python 2, including better Unicode support and a print function.
Key Features
Python offers an interactive interpreter, which is useful for learning and rapid prototyping. It has a large and active community that contributes to continuous improvement and a wealth of educational resources. The language is open source and managed by the Python Software Foundation.
Common applications include scripting, system administration, network programming, and the development of desktop and web applications. Frameworks such as Django and Flask are popular for web development, while libraries like scikit-learn support machine learning workflows.