发帖
雷达卡
摘要翻译：
本文研究了协方差矩阵自适应进化策略（CMA-ES）的一个变体的收敛性。我们的研究是基于最近的理论基础，即纯秩mu更新CMA-ES在高斯分布的参数空间上进行自然梯度下降。我们推导了自然梯度法的一种新的变体，即沿自然梯度更新高斯分布的参数，以改进参数空间上新定义的函数。我们研究了单调函数与凸二次函数复合的算法。我们证明了我们的算法自适应协方差矩阵，使其与原目标函数的Hessian的逆成正比。我们还给出了协方差矩阵自适应的速度和参数收敛的速度。我们介绍了一种用有限样本逼近自然梯度的随机算法，并给出了一些仿真结果，以评估在有限样本下随机算法逼近确定性理想梯度的精度，以及我们的算法和CMA-ES在性能上的相似性。
---
英文标题：
《Analysis of a Natural Gradient Algorithm on Monotonic
Convex-Quadratic-Composite Functions》
---
作者：
Youhei Akimoto (INRIA Saclay - Ile de France)
---
最新提交年份：
2017
---
分类信息：
一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
--
一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
--
---
英文摘要：
In this paper we investigate the convergence properties of a variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Our study is based on the recent theoretical foundation that the pure rank-mu update CMA-ES performs the natural gradient descent on the parameter space of Gaussian distributions. We derive a novel variant of the natural gradient method where the parameters of the Gaussian distribution are updated along the natural gradient to improve a newly defined function on the parameter space. We study this algorithm on composites of a monotone function with a convex quadratic function. We prove that our algorithm adapts the covariance matrix so that it becomes proportional to the inverse of the Hessian of the original objective function. We also show the speed of covariance matrix adaptation and the speed of convergence of the parameters. We introduce a stochastic algorithm that approximates the natural gradient with finite samples and present some simulated results to evaluate how precisely the stochastic algorithm approximates the deterministic, ideal one under finite samples and to see how similarly our algorithm and the CMA-ES perform.
---
PDF链接：
https://arxiv.org/pdf/1204.4141
京公网安备 11010802022788号
