后半句说的是梯度下降法可以实现的内容
xs <- seq(0,4,len=20) # create some values
# define the function we want to optimize
f <- function(x) {
1.2 * (x-2)^2 + 3.2
}
# plot the function
plot(xs , f (xs), type="l",xlab="x",ylab=expression(1.2(x-2)^2 +3.2))
# calculate the gradeint df/dx
grad <- function(x){
1.2*2*(x-2)
}
# df/dx = 2.4(x-2), if x = 2 then 2.4(2-2) = 0
# The actual solution we will approximate with gradeint descent
# is x = 2 as depicted in the plot below
lines (c (2,2), c (3,8), col="red",lty=2)
text (2.1,7, "Closedform solution",col="red",pos=4)
# gradient descent implementation
x <- 0.1 # initialize the first guess for x-value
xtrace <- x # store x -values for graphing purposes (initial)
ftrace <- f(x) # store y-values (function evaluated at x) for graphing purposes (initial)
stepFactor <- 0.6 # learning rate 'alpha'
for (step in 1:100) {
x <- x - stepFactor*grad(x) # gradient descent update
xtrace <- c(xtrace,x) # update for graph
ftrace <- c(ftrace,f(x)) # update for graph
}
lines ( xtrace , ftrace , type="b",col="blue")
text (0.5,6, "Gradient Descent",col="blue",pos= 4)
# print final value of x
print(x) # x converges to 2.0
扫码加好友，拉您进群
全部版块
我的主页
收藏
