全局Optimization的受控粒子滤波
A Controlled Particle Filter for Global Optimization
摘要：
引入粒子滤波器来数值地近似全局最优化问题的解。这项工作的理论意义来自其变分方面：（i）建议的粒子滤波器是一个受控的相互作用的粒子系统，其中的控制输入代表的平均场型最优控制问题的解决方案;和（ii）相关的密度运输被证明是一个梯度流（最速下降）的最优值函数，相对于Kullback-Leibler发散。粒子滤波器的最优控制构造与经典的基于重要性采样的方法有很大的不同。有几个实际的优点：（i）的复活，再生，死亡或出生的粒子被避免;（ii）模拟方差可以潜在地减少通过应用反馈控制原则;和（iii）参数近似自然出现作为一个特殊的情况。后者还提出了系统的数值逼近的最优控制法的方法。理论结果与数值例子进行了说明。
英文摘要：
A particle filter is introduced to numerically approximate a solution of the global optimization problem. The theoretical significance of this work comes from its variational aspects: (i) the proposed particle filter is a controlled interacting particle system where the control input represents the solution of a mean-field type optimal control problem; and (ii) the associated density transport is shown to be a gradient flow (steepest descent) for the optimal value function, with respect to the Kullback--Leibler divergence. The optimal control construction of the particle filter is a significant departure from the classical importance sampling-resampling based approaches. There are several practical advantages: (i) resampling, reproduction, death or birth of particles is avoided; (ii) simulation variance can potentially be reduced by applying feedback control principles; and (iii) the parametric approximation naturally arises as a special case. The latter also suggests systematic approaches for numerical approximation of the optimal control law. The theoretical results are illustrated with numerical examples.
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