不可微Optimization的自适应随机搜索
Gradient-Based Adaptive Stochastic Search for Non-Differentiable Optimization
摘要：
本文提出了一种求解一般小结构最优化问题的随机搜索算法。该算法通过在解空间上从参数化分布模型中随机抽取候选解，迭代地找到高质量的解。其基本思想是将原问题（可能是不可微的）转化为参数化抽样分布的参数空间上的可微最优化问题，然后使用直接梯度搜索方法寻找改进的抽样分布。因此，该算法结合了随机搜索的鲁棒性，考虑人口的候选解决方案与相对较快的收敛速度的经典梯度法，通过利用局部可微结构。我们分析了算法的收敛性和收敛速度，并进行数值研究，以说明其性能。
英文摘要：
In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized distribution model over the solution space. The basic idea is to convert the original (possibly non-differentiable) problem into a differentiable optimization problem on the parameter space of the parameterized sampling distribution, and then use a direct gradient search method to find improved sampling distributions. Thus, the algorithm combines the robustness feature of stochastic search from considering a population of candidate solutions with the relative fast convergence speed of classical gradient methods by exploiting local differentiable structures. We analyze the convergence and converge rate properties of the proposed algorithm, and carry out numerical study to illustrate its performance.
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