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Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization

机译：平行顺序蒙特卡罗用于随机梯度无凸不应渗透

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摘要

We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth-order optimization algorithm which demands only the capability to evaluate small subsets of components of the cost function. It can be depicted as a bank of samplers that generate particle approximations of several sequences of probability measures. These measures are constructed in such a way that they have associated probability density functions whose global maxima coincide with the global minima of the original cost function. The algorithm selects the best performing sampler and uses it to approximate a global minimum of the cost function. We prove analytically that the resulting estimator converges to a global minimum of the cost function almost surely and provide explicit convergence rates in terms of the number of generated Monte Carlo samples and the dimension of the search space. We show, by way of numerical examples, that the algorithm can tackle cost functions with multiple minima or with broad "flat" regions which are hard to minimize using gradient-based techniques.
机译：我们介绍并分析并分析并分析并行顺序蒙特卡罗方法，了解了优化问题的数值解决方案，涉及最小化成本函数，该功能包括许多单独组件的总和。所提出的方案是一种随机零顺序优化算法，该算法仅需要评估成本函数的小亚组件的能力。它可以被描绘为一组采样器，产生几个概率措施序列的粒子近似。这些措施以这样的方式构建，使得它们具有相关的概率密度函数，其全球最大值与原始成本函数的全局最小值相一致。该算法选择最佳的执行采样器，并使用它来近似于成本函数的全局最小值。我们在分析上证明了所得估计器几乎肯定地将成本函数的全球最小值收敛并提供显式的收敛速率，并提供所产生的蒙特卡罗样本的数量和搜索空间的维度。我们通过数值示例显示算法可以用多个最小值或具有广泛的“平坦”区域来解决成本函数，这很难使用基于梯度的技术最小化。

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