# Note Stack 笔记堆栈

## 无处安放的笔记

Posted by tianchen on August 6, 2020

# Paper Stack 文章堆栈

• 撒豆子算面积的实验

### 2020-03-24 Gumble Softmax

• 从VAE(连续分布采样的求导)，加入一个Gumble噪声(包含了参数的信息)，首先从Gaussian中采样，带入值
• 对于离散分布，加一个Argmax->Softmax

### 2021-01-03 NES

• Keys

a family of black-box optimization algorithms use natural grad to update the parameterized distribution in the direction of higher expected fitness

• Source - Jurgen

• Motivation

• Methodoly

Iteratively update the searched distribution by using estimated grad on its distribution param(e.g. \miu & \sigma of gaussian), iter stops while the criterion is met.

what is search space? what is fitness?

however, to locate a quadratic optimum, should be at least quatratic, since 1-order methods will be unstable the update is not scale-invariant this does not occur in general grad-based case, since here the grad controls both the position and the variance of distribution over the same search space dimension this problem is solved with the natural gradient

how to make it a constraint optimization

natural gradient is proposed in the ml field to help mitigate the slow convergence in plataeu landscape / ridges(山岭，山脊) the plain grad \delta{J} represent the steepest ascent(in the space of the actual param \theta) when the learning-step \epsilon is small, the problem could be reformed as finding a new distribution with param chosen from the hypersphere of radius \epsilon and center \theta that maximize the plain grad \delta{J}. so the Enculidean distance is used for measuring the distance between the distribution, so the update is dependent of the parameterization of the distribution. the key of natural is to remove this dependence, finding a natural distance(e.g. KL distance), reduce it to the constraint optimizaiton **use the natural grad instead of the steepest grad for optimization*

1. Fitness shaping - make the distribution invariante to (arbitary but order-preserving transformation)

what is order? simply make the ranking of the fiteness function of the population no change?

not so crucial.

meta-learning based(sample new \theta, if quality significantly better, continue with \theta_hat), apply hill-climbing and the Mann-Witney U-Test

1. rotation-invariant distribution

local-natural coordinate sampling from radical distribution

• Experiment

• Ideas

multi-variant gaussian, fisher information matrix

• closely related to CMA-ES(Convariance Matrix Adaptation Evolutional Strategy)