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I have trained my neural network model with optimizers such as RMSProp, AdaGrad, Momentum, and Adam.

Currently, after running the code, I have printed out the Train and Test Accuracy of every epoch (50 in my case). However, I would like to know how should I determine which of these optimizers performs the best?

Does a higher train accuracy at the last epoch determine which is best or would a higher test accuracy do so? Also, I observed that when using the Momentum optimizer, the model train accuracy reached its' highest around 0.91 in the 16th epoch compared to the other optimizer.

Hence, would that conclude that the Momentum optimizer performs best in this case?

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High training score is not an indication of model performance, high test score is. Also, a faster convergence to the same, or better test score is an indication of optimizer performance.

Therefore, if Momentum optimizer reaches a better test score faster, it definitely means that it is the best out of those tested optimizers.

As a side note, be careful about the choice of "score", for example using "accuracy" for imbalanced classes is not a good choice, since it equates %1 error in a class with 100 members to 10% error in a class with 10 members. If classes are equally important, i.e. 1% error is equally bad for all classes, macro-f1 and AUC would be better replacements.

An important note: when we use a score to select a hyper-parameter or an optimizer, final model will be affected, thus, that score would be called validation score, not test score.

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