随机全局优化作为滤波问题
Stochastic global optimization as a filtering problem
AI总结：
将随机全局优化重新表述为滤波问题，利用粒子滤波器聚焦有前途的解，在参数指数密度估计中比朴素全局优化更快收敛。
摘要：
我们将随机全局优化重新表述为滤波问题。这种重新表述的动机来自这样一个事实：对于许多优化问题，我们无法精确评估要优化的目标函数。同样，我们可能无法精确评估迭代优化算法中涉及的函数。例如，我们可能只能通过蒙特卡洛采样获得函数的噪声测量或统计估计。这使得迭代优化算法表现得像随机映射。朴素全局优化相当于演化这个随机映射的一组实现，并选择具有最佳属性的实现。这激发了使用滤波技术来聚焦于比其他更有前途的实现。特别地，我们提出了全局优化的滤波重新表述，作为顺序重要性采样方法的一个特例，称为粒子滤波器。粒子滤波器日益流行的基础是其实现的简单性和灵活性。对于参数指数密度估计问题，我们利用粒子滤波器的灵活性构建了一个随机全局优化算法，该算法比朴素全局优化更快地收敛到最优解。提供了几个例子来证明该方法的效率。
英文摘要：
We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be optimized. Similarly, we may not be able to evaluate exactly the functions involved in iterative optimization algorithms. For example, we may only have access to noisy measurements of the functions or statistical estimates provided through Monte Carlo sampling. This makes iterative optimization algorithms behave like stochastic maps. Naive global optimization amounts to evolving a collection of realizations of this stochastic map and picking the realization with the best properties. This motivates the use of filtering techniques to allow focusing on realizations that are more promising than others. In particular, we present a filtering reformulation of global optimization in terms of a special case of sequential importance sampling methods called particle filters. The increasing popularity of particle filters is based on the simplicity of their implementation and their flexibility. For parametric exponential density estimation problems, we utilize the flexibility of particle filters to construct a stochastic global optimization algorithm which converges to the optimal solution appreciably faster than naive global optimization. Several examples are provided to demonstrate the efficiency of the approach.
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