Thank you very much for an interesting discussion.
I'm sorry if my English is not fluent.
Based on the professor's answer of
this question, here is my thought:
I think I will first get my try with 3rd order polynomial model on the training set and then test it on the first "validation" set. If I am satisfied with the test result then I stop the process and choose 3rd order one. If I find the 3rd order is overfitting (low training error, high test error) I will get my next try with 2nd order, however if I find the 3rd order is underfitting (high training error, high test error) I will get my next try with 5th order. As you may notice, I am trying to use binary search algorithm here.
Obviously, I find it's hard to determine whether a result is satisfied enough, to me it looks like it depends on the specific application situation.
Whatever the model is my next try, I will obviously train it all the training set and then validate it on the first validation set (now the first validation set is no test set anymore).
In the case my next try is 2nd order:
 If am satisfied with the result then I will stop here and choose 2nd order one.
 If I find the 2nd order is overfitting then I will try to regularize the 2nd order.
 If I find the 2nd order is underfitting then I will try to regularize the 3rd order.
In the case my next try is 5th order, I can make the similar decisions.
Now if I am going to have to regularized one of the three models, I will also combine the training set with the first validation set, use the binary search algorithm as described above on the regularization parameters.
In this case, maximum number of combinations of H and lambda need to be validated using binary search is quite small: Only 5 combinations.
Finally I will have the best choice of model and parameter in my thought. It would be great if I have a test set to test this final choice of mine.

If I have a choice on how to divide the dataset, I will divide it into two parts: One part for training and one part for testing. The test set will be locked and will be used for only one final hypothesis to report the performance (with tight bound) of the final hypothesis to the customer.
Then I will divide the training set in to two parts: One part for the first crossvalidation to choose model and second part for the second crossvalidation to choose regularization parameter. For this process, I will use the same binary search idea as described above.

The book also has this statement on validation:
Quote:
In the case of validation, making a choice for few parameters does not overly contaminate the validation estimate of , even if the VC guarantee for these estimates is too weak.

Of course, I am not sure how to interpret the "few" word here.