论文标题
降低降低技术，用于无效的函数的全局优化，有效尺寸较低
A dimensionality reduction technique for unconstrained global optimization of functions with low effective dimensionality
论文作者
论文摘要
我们研究了具有较低有效维度的功能的无约束的全局优化，这些功能沿特定（未知）线性子空间恒定。通过随机嵌入，在[Wang等人的[Wang等人》中扩展了随机子空间嵌入的技术。 Jair，55（1）：361--387，2016]，我们研究了与任何全球最小化算法兼容的全局优化框架（REGO）框架的通用随机嵌入。在雷戈（Rego）内，与原始的，潜在的大规模优化问题相比，在降低的空间中制定并解决了界限的高斯随机，低维问题。我们为Rego在解决原始的，低的有效差异问题方面的成功提供了新颖的概率界限，这些问题表明了（潜在的大）环境维度的独立性及其对有效和随机嵌入子空间的维度的精确依赖性。这些结果通过提供减少的最小化器及其欧几里得规范的确切分布以及问题所需的一般假设，从而显着改善了现有的理论分析。我们通过使用三种类型的全局优化求解器对Rego进行广泛的数值测试来验证我们的理论发现，这说明了与各自求解器的全维应用相比，REGO的可伸缩性提高了。
We investigate the unconstrained global optimization of functions with low effective dimensionality, that are constant along certain (unknown) linear subspaces. Extending the technique of random subspace embeddings in [Wang et al., Bayesian optimization in a billion dimensions via random embeddings. JAIR, 55(1): 361--387, 2016], we study a generic Random Embeddings for Global Optimization (REGO) framework that is compatible with any global minimization algorithm. Instead of the original, potentially large-scale optimization problem, within REGO, a Gaussian random, low-dimensional problem with bound constraints is formulated and solved in a reduced space. We provide novel probabilistic bounds for the success of REGO in solving the original, low effective-dimensionality problem, which show its independence of the (potentially large) ambient dimension and its precise dependence on the dimensions of the effective and randomly embedding subspaces. These results significantly improve existing theoretical analyses by providing the exact distribution of a reduced minimizer and its Euclidean norm and by the general assumptions required on the problem. We validate our theoretical findings by extensive numerical testing of REGO with three types of global optimization solvers, illustrating the improved scalability of REGO compared to the full-dimensional application of the respective solvers.
