Why does the Hyperparameter optimization method GridSearch suffer from the curse of dimensionality? An example accompanied by explanation is needed.
 A: With a gridsearch you just try a set of values for your parameters and look at which value the objective function is largest (or smallest). Lets say you have one parameter and want to try for the values $1, 2, 3, 4, 5, 6, 7, 8, 9, 10$. (this is not realistic, normally you try many more possible values). In this example you need to compute the objective function 10 times.
Lets say there is a second parameter. Now you need to try the values: 
$(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8), (1,9), (1,10), (2,1), (2,2), (2,3), (2,4), (2, 5), (2,6), (2,7), (2,8), (2,9), (2,10), \cdots , (10,1), (10,2), (10,3), (10,4), (10,5), (10,6), (10,7), (10,8), (10,9), (10,10)$. 
So now you need to compute the objective function $10 \times 10 = 100$ times. If you have a third parameter you would end up with $10^3=1000$ evaluations, etc. 
If we use a more realist number of tries per parameter, say 1000, then we end up with a $1000^1=1000$ evaluations for one parameter, $1000^2=1,000,000$ evaluations for two parameters, $1000^3=1,000,000,000$ evaluations for three parameters, etc. You can see that you can quickly end up with an unmanageable number of evaluations.
