Is there a general conclusion on what one should expect from hyperparameter tuning? For instance, is it always the case that hyperparameter can only increase the performance from OK to good (say 0.75 r-score to 0.90) or is it possible to see a jump from bad to good (0.1 to 0.9) after hyperparameter tuning?
Let's say I'm working on a problem with CNN. I started by using a shallow fully connected architecture which gives me only an r-score of 0.3, and there is clearly a linear relation between the target and predictions. I'm now at the point to decided whether I should invest time on tuning the hyperparameters or is this already a flag that something else is wrong and I need to investigate on more fundamental things such as my dataset?
I understand this might be dependant on the specific problem but I'd like to hear you ideas.