Relationship between train and test error
First of all be very clear with the use of the Training set, Validation set and  Testing set. These play a crucial part in  tuning your DL model. Usually, a validation dataset is used for keeping a check over the model during the training. An intutive observations are noted with the training validation and testing accuracy during data fitting:


If the model is having high validation accuracy and low training accuracy, it is an underfit model.
If the model has higher training accuracy and low validation accuracy, it is overfit.


Bias-variance trade-off problem is a central problem of supervised machine learning algorithms.

The bias–variance decomposition is a way of analyzing a learning algorithm's expected generalization error with respect to a particular problem as a sum of three terms, the bias, variance, and a quantity called the irreducible error, resulting from noise in the problem itself. 

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