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Annealing Adaptive Search, Cross-Entropy, and Stochastic Approximation in Global Optimization

机译：全局优化中的退火自适应搜索，交叉熵和随机逼近

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The Annealing Adaptive Search (AAS) algorithm for global optimization searches the solution space by sampling from a sequence of Boltzmann distributions. For a class of optimization problems, it has been shown that the complexity of AAS increases at most linearly in the problem dimension. However, despite its desirable property, sampling from a Boltzmann distribution at each iteration of the algorithm remains a practical challenge. Prior work to address this issue has focused on embedding Markov chain-based sampling techniques within the AAS framework. In this article, based on ideas from the recent Cross-Entropy method and Model Reference Adaptive Search, we propose an algorithm, called Model-based Annealing Random Search (MARS), that complements prior work by sampling solutions from a sequence of surrogate distributions that iteratively approximate the target Boltzmann distributions. We establish a novel connection between MARS and the well-known Stochastic Approximation method. By exploiting this connection, we prove the global convergence of MARS and characterize its asymptotic convergence rate behavior. Our empirical results indicate promising performance of the algorithm in comparison with some of the existing methods.
机译：用于全局优化的退火自适应搜索（AAS）算法通过从一系列Boltzmann分布中进行采样来搜索解空间。对于一类优化问题，已经表明AAS的复杂性在问题维度上最多呈线性增加。但是，尽管具有理想的性能，但是在算法的每次迭代中从玻耳兹曼分布进行采样仍然是一个实际的挑战。解决该问题的先前工作着重于将基于马尔可夫链的采样技术嵌入AAS框架。在本文中，基于最新的交叉熵方法和模型参考自适应搜索的思想，我们提出了一种算法，称为基于模型的退火随机搜索（MARS），该算法通过从一系列替代分布中采样解决方案来对先前的工作进行补充迭代近似目标玻尔兹曼分布。我们在MARS和著名的随机近似方法之间建立了一种新颖的联系。通过利用这种联系，我们证明了MARS的全局收敛性，并描述了其渐近收敛速率行为。我们的经验结果表明，与某些现有方法相比，该算法的性能令人鼓舞。

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