How to monitor loss & val_loss at the same time to avoid overfitting Neural network to either train set or test set?

You can choose between two approaches:

1. Create a custom metric to record the metric you want, by subclassing tf.keras.metrics.Metric. See https://www.tensorflow.org/api_docs/python/tf/keras/metrics/Metric for an example.
   You can then use your metric in standard callbacks e.g. EarlyStopping()

2. Create a custom callback to do the calculation (and take the action) you want, by subclassing tf.keras.callbacks.CallBack. See https://www.tensorflow.org/guide/keras/custom_callback for how to do this.

I have an answer to a problem that is pretty similar to this, here.

Basically, it is not possible to monitor multiple metrics with keras callbacks. However you could define a custom callback (see the documentation for more info) that can access the logs at each epoch and do some operations.

Let's say if you want to monitor loss and val_loss you can do something like this:

class CombineCallback(tf.keras.callbacks.Callback):

    def __init__(self, **kargs):
        super(CombineCallback, self).__init__(**kargs)

    def on_epoch_end(self, epoch, logs={}):
        logs['combine_metric'] = logs['val_loss'] + logs['loss']

Side note: the most important thing in my opinion is to monitor the validation loss. Train loss of course will keep dropping, so it is not really that meaningful to observe. If you really want to monitor them both I suggest you adding a multiplicative factor and give more weight to validation loss. In this case:

class CombineCallback(tf.keras.callbacks.Callback):

    def __init__(self, **kargs):
        super(CombineCallback, self).__init__(**kargs)

    def on_epoch_end(self, epoch, logs={}):
        factor = 0.8
        logs['combine_metric'] = factor * logs['val_loss'] + (1-factor) * logs['loss']

Then you can use it like this:

model.fit(
    ...
    callbacks=[CombineCallback()],
)

Also you can draw more inspiration here.

Below is a Keras custom callback that should do the job. The callback monitors both the training loss and the validation loss. The form of the callback is callbacks=[SOMT(model, train_thold, valid_thold)] where:

• model is the name of your complied model
• train_thold is a float. It is the value of accuracy (in Percent) that must be achieved by the model in order to conditionally stop training
• valid_threshold is a float. It is the value of validation accuracy (in Percent) that must be achieved by the model in order to conditionally stop training Note to stop training BOTH the train_thold and valid_thold must be exceeded in the SAME epoch.
  If you want to stop training based soley on the training accuracy set the valid_thold to 0.0.
  Similarly if you want to stop training on just validation accuracy set train_thold= 0.0.

Note if both thresholds are not achieved in the same epoch training will continue until the value of epochs specified in model.fit is reached.
For example lets take the case that you want to stop training when the
training accuracy has reached or exceeded 95 % and the validation accuracy has achieved at least 85%
then the code would be callbacks=[SOMT(my_model, .95, .85)]

class SOMT(keras.callbacks.Callback):
    def __init__(self, model,  train_thold, valid_thold):
        super(SOMT, self).__init__()
        self.model=model        
        self.train_thold=train_thold
        self.valid_thold=valid_thold
        
    def on_train_begin(self, logs=None):
        print('Starting Training - training will halt if training accuracy achieves or exceeds ', self.train_thold)
        print ('and validation accuracy meets or exceeds ', self.valid_thold) 
        msg='{0:^8s}{1:^12s}{2:^12s}{3:^12s}{4:^12s}{5:^12s}'.format('Epoch', 'Train Acc', 'Train Loss','Valid Acc','Valid_Loss','Duration')
        print (msg)                                                                                    
            
    def on_train_batch_end(self, batch, logs=None):
        acc=logs.get('accuracy')* 100  # get training accuracy 
        loss=logs.get('loss')
        msg='{0:1s}processed batch {1:4s}  training accuracy= {2:8.3f}  loss: {3:8.5f}'.format(' ', str(batch),  acc, loss)
        print(msg, '\r', end='') # prints over on the same line to show running batch count 
        
    def on_epoch_begin(self,epoch, logs=None):
        self.now= time.time()
        
    def on_epoch_end(self,epoch, logs=None): 
        later=time.time()
        duration=later-self.now 
        tacc=logs.get('accuracy')           
        vacc=logs.get('val_accuracy')
        tr_loss=logs.get('loss')
        v_loss=logs.get('val_loss')
        ep=epoch+1
        print(f'{ep:^8.0f} {tacc:^12.2f}{tr_loss:^12.4f}{vacc:^12.2f}{v_loss:^12.4f}{duration:^12.2f}')
        if tacc>= self.train_thold and vacc>= self.valid_thold:
            print( f'\ntraining accuracy and validation accuracy reached the thresholds on epoch {epoch + 1}' )
            self.model.stop_training = True # stop training