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I am trying to replicate (a way smaller version) of the AlphaGo Zero system. However, in the network model, I am having a problem. The loss function I am supposed to implement is the following:

$$l = (z - v)^2 - \pi^T log(p) + c ||\theta||^2$$

Where:

  • $z$ is the label (a real value between -1 and 1) of one of the two heads of network and $v$ is this value predicted by the network.
  • $\pi$ is the label of a distribution probability over all actions and $p$ is the distribution probability over all actions predicted by the network.
  • $c$ is the L2 regularization parameter.

I pass to the network a list of channels (representing the game state) and an array (same size of the $\pi$ and $p$) representing which actions are indeed valid (by putting 1 if valid, 0 otherwise).

As you can see, the loss function uses both the target and the network predictions for the calculation. But after extensive search, when implementing my custom loss function, I can only pass as parameter y_true and y_pred even though I have two "y_true's" and two "y_pred's". I have tried using indexing to get those values but I'm pretty sure it is not working.

The modeling of the network and the custom loss function is in the code below:

def custom_loss(y_true, y_pred):

    # I am pretty sure this does not work

    output_prob_dist = y_pred[0]
    output_value = y_pred[1] 
    label_prob_dist = y_true[0]
    label_value = y_pred[1]

    mse_loss = K.mean(K.square(label_value - output_value), axis=-1)
    cross_entropy_loss = K.dot(K.transpose(label_prob_dist), output_prob_dist)

    return mse_loss - cross_entropy_loss

def define_model():
    """Neural Network model implementation using Keras + Tensorflow."""
    state_channels = Input(shape = (5,5,6), name='States_Channels_Input')
    valid_actions_dist = Input(shape = (32,), name='Valid_Actions_Input')

    conv = Conv2D(filters=10, kernel_size=2, kernel_regularizer=regularizers.l2(0.0001), activation='relu', name='Conv_Layer')(state_channels)
    pool = MaxPooling2D(pool_size=(2, 2), name='Pooling_Layer')(conv)
    flat = Flatten(name='Flatten_Layer')(pool)

    # Merge of the flattened channels (after pooling) and the valid action
    # distribution. Used only as input in the probability distribution head.
    merge = concatenate([flat, valid_actions_dist])

    #Probability distribution over actions
    hidden_fc_prob_dist_1 = Dense(100, kernel_regularizer=regularizers.l2(0.0001), activation='relu', name='FC_Prob_1')(merge)
    hidden_fc_prob_dist_2 = Dense(100, kernel_regularizer=regularizers.l2(0.0001), activation='relu', name='FC_Prob_2')(hidden_fc_prob_dist_1)
    output_prob_dist = Dense(32, kernel_regularizer=regularizers.l2(0.0001), activation='softmax', name='Output_Dist')(hidden_fc_prob_dist_2)

    #Value of a state
    hidden_fc_value_1 = Dense(100, kernel_regularizer=regularizers.l2(0.0001), activation='relu', name='FC_Value_1')(flat)
    hidden_fc_value_2 = Dense(100, kernel_regularizer=regularizers.l2(0.0001), activation='relu', name='FC_Value_2')(hidden_fc_value_1)
    output_value = Dense(1, kernel_regularizer=regularizers.l2(0.0001), activation='tanh', name='Output_Value')(hidden_fc_value_2)

    model = Model(inputs=[state_channels, valid_actions_dist], outputs=[output_prob_dist, output_value])

    model.compile(loss=custom_loss, optimizer='adam', metrics=['accuracy'])

    return model



# In the main method
model = define_model()
# ...
# MCTS routine to collect the data for the network input
# ...

x_train = [channels_input, valid_actions_dist_input]
y_train = [dist_probs_label, who_won_label]

model.fit(x_train, y_train, epochs=10)

In short, my question is: how do I correctly implement this custom loss function that uses both the network outputs and label values of the network?

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You could check this answer.

If you solved, please provide an update in your post. It might be useful for all of us.

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