how to implement walk forward testing in sklearn?
I think you could use a Time Series Split either instead of your own implementation or as a basis for implementing a CV method which is exactly as you describe it.
After digging around a bit, it seems like someone added a max_train_size to the TimeSeriesSplit in this PR which seems like it does what you want.
I did some work regarding all this some months ago.
You could check it out in this question/answer:
Rolling window REVISITED - Adding window rolling quantity as a parameter- Walk Forward Analysis
My opinion is that you should try to implement your own GridSearchWalkForwardTest. I used GridSearch once to do the training and implemented the same GridSearch myself and I didn't get the same results, eventhough I should.
What I did at the end is using my own function. You have more control over the training and test set and you have more control over the parameters you train.