论文标题
具有替代功能的信息几何优化算法的单调改进
Monotone Improvement of Information-Geometric Optimization Algorithms with a Surrogate Function
论文作者
论文摘要
通常采用替代功能来减少优化目标函数评估的数量。但是，在进化方法中使用替代模型的效果尚未得到理论上的研究。本文理论上使用替代函数分析了信息几何优化框架。在候选抽样分布下的预期目标函数的值用作算法进度的度量。我们假设维持替代函数，以便肯德尔等级相关系数的替代函数与候选抽样分布下的目标函数之间的人口版本大于或等于预定义的阈值。我们证明，如果阈值足够接近一个，则使用这种替代功能的信息几何优化会导致预期目标函数值的单调降低。分析了可接受的阈值值，该阈值是通过高斯分布实例化的信息几何优化的情况，即，在凸二次目标函数上，即$ $ $ $ $ $ $更新CMA-ES。作为Kendall等级相关系数的替代方案，我们研究了根据目标函数和替代功能分配给候选解决方案的权重之间的Pearson相关系数。
A surrogate function is often employed to reduce the number of objective function evaluations for optimization. However, the effect of using a surrogate model in evolutionary approaches has not been theoretically investigated. This paper theoretically analyzes the information-geometric optimization framework using a surrogate function. The value of the expected objective function under the candidate sampling distribution is used as the measure of progress of the algorithm. We assume that the surrogate function is maintained so that the population version of the Kendall's rank correlation coefficient between the surrogate function and the objective function under the candidate sampling distribution is greater than or equal to a predefined threshold. We prove that information-geometric optimization using such a surrogate function leads to a monotonic decrease in the expected objective function value if the threshold is sufficiently close to one. The acceptable threshold value is analyzed for the case of the information-geometric optimization instantiated with Gaussian distributions, i.e., the rank-$μ$ update CMA-ES, on a convex quadratic objective function. As an alternative to the Kendall's rank correlation coefficient, we investigate the use of the Pearson correlation coefficient between the weights assigned to candidate solutions based on the objective function and the surrogate function.
