in python:

Gradient Descent$-$

Objective : Implement the Gradient Descent to minimize the cost function ofa synthetic dataset generated froma non$-$linear function.

$1.$Generate Shynthetic Data

$-$generate $200$ randomly generated values of X between $-10$ and $10.$

$-$generate the target variable y using the function $5$x$^4+2$x$^3+9$x $+12.$ This is your model.

$-$ The bias term Xbias is initialized to $1.$ in python

$2.$ Implant Gradient Descent

$-$Use the variables name compute$\_$error to calculate the Root Mean Squared Error$($RMSE$)$ between the predicted and actual target values.

$-$define a function gradient descent to perform Grafient Descent and return the optimized weights, theta.

$-$ Initialize the weights randomly.

$3.$ Hyperparameters

$-$Run the existencexperiment with different learning rates$($LR$)$ and observe how it affects the convergence of the algorithm. Use: LR:$0\mathrm{.}001,0\mathrm{.}01,0\mathrm{.}0005.$

$-$Display the final RMSE for each learning rate.

$4.$ Submission

$-$ Final output: should look like this: Learning Rate: $0\mathrm{.}001$; RMSE: XXXX$.$XXXX$,$ where this is the computed error: Repeat for all $3$ LRs$.$

Example:

Learning Rate: $0\mathrm{.}001$; RMSE: $3523\mathrm{.}1301$

Learning Rate: $0\mathrm{.}01$; RMSE: $9813\mathrm{.}8717$

Learning Rate: $0\mathrm{.}0005$; RMSE: $1332\mathrm{.}2333$