Lower cost function error not means better accuracy.
The error of the cost function represents how well your model is learning/able to learn with respect to your training examples.
Now the question is ,
Is the model learning something that I expect it to learn?
It can show very low learning curves error but when you actually testing the results (Accuracy) you are getting wrong detection's , this is called high variance.
The best is to monitor the both learning error and accuracy for each epoch/iteration, While cost function error goes down and accuracy goes up keep training, otherwise stop (:
The accuracy is not good enough? check :
1. do I have high variance problem ? add more training examples to generalize the learning (better find more examples which reminds the problems where your model fails on).
- Do I have high bias problem ? my model is pure or to complex , need to fix it / try something else.
Good luck (: