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I am running a grid search for a binary classifier. Each model will receive a list of parameters and then that model will be run 20 times (20 epochs.) Many times the first epoch will have a high val_acc and then the val_acc will decrease as the epochs move toward 20. Should I care that the val_accs are decreasing? Or can I just take the highest val_acc model and use that as the model?

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The validation accuracy is perhaps the most important metric, in that it is a measure of how well your model has generalized, and how well it will perform on new unseen data. If it is always decreasing your model is probably over fitting. Add more dropout layers, more/better training & validation data, or reevaluate your overall approach to the problem. To directly answer the question, yes you should care, your model is not learning. Good luck.

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