Gaussian Process based Bayesian Optimization is a well-known sample efficient
sequential strategy for globally optimizing black-box, expensive, and
multi-extremal functions. The role of the Gaussian Process is to provide a
probabilistic approximation of the unknown function, depending on the
sequentially collected observations, while an acquisition function drives the
choice of the next solution to evaluate, balancing between exploration and
exploitation, depending on the current Gaussian Process model. Despite the huge
effort of the scientific community in defining effective
exploration-exploitation mechanisms, we are still far away from the master
acquisition function. This paper merges the most relevant results and insights
from both algorithmic and human search strategies to propose a novel
acquisition function, mastering the trade-off between explorative and
exploitative choices, adaptively. We compare the proposed acquisition function
on a number of test functions and against different state-of-the-art ones,
which are instead based on prefixed or random scheduling between exploration
and exploitation. A Pareto analysis is performed with respect to two
(antagonistic) goals: convergence to the optimum and exploration capability.
Results empirically prove that the proposed acquisition function is almost
always Pareto optimal and also the most balanced trade-off between the two
goals.

通过融合算法和人类搜索策略的关键成果和见解，该论文提出了一种新的获得函数，掌握探索和开发之间的权衡，可以自适应地选择下一个解决方案，表现出卓越的性能

贝叶斯优化中探索 - 利用权衡的掌握

Mastering the exploration-exploitation trade-off in Bayesian  Optimization

We propose a sparse regression method capable of discovering the governing
partial differential equation(s) of a given system by time series measurements
in the spatial domain. The regression framework relies on sparsity promoting
techniques to select the nonlinear and partial derivative terms terms of the
governing equations that most accurately represent the data, bypassing a
combinatorially large search through all possible candidate models. The method
balances model complexity and regression accuracy by selecting a parsimonious
model via Pareto analysis. Time series measurements can be made in an Eulerian
framework where the sensors are fixed spatially, or in a Lagrangian framework
where the sensors move with the dynamics. The method is computationally
efficient, robust, and demonstrated to work on a variety of canonical problems
of mathematical physics including Navier-Stokes, the quantum harmonic
oscillator, and the diffusion equation. Moreover, the method is capable of
disambiguating between potentially non-unique dynamical terms by using multiple
time series taken with different initial data. Thus for a traveling wave, the
method can distinguish between a linear wave equation or the Korteweg-deVries
equation, for instance. The method provides a promising new technique for
discovering governing equations and physical laws in parametrized
spatio-temporal systems where first-principles derivations are intractable.

提出了一种基于稀疏回归的方法，能够通过空间域中的时间序列测量发现给定系统的主要偏微分方程，该方法通过稀疏促进技术来选择最准确地表示数据的非线性和偏导数术语，同时考虑模型复杂性和回归精度的平衡，通过帕累托分析选择简洁的模型，并在多种数学物理问题中进行了演示。