Now we'll see how can we find the optimal parameters of our neural network with Reptile.

First, we initialize the necessary variables:

#number of epochs i.e training iterations
num_epochs = 100

#number of samples i.e number of shots
num_samples = 50 

#number of tasks
num_tasks = 2

#number of times we want to perform optimization
num_iterations = 10

#mini btach size
mini_batch = 10 

Then, we start the TensorFlow session:

with tf.Session() as sess:
    
    sess.run(init)
    

For the number of epochs:

    for e in range(num_epochs):
        
        #for each task in batch of tasks
        for task in range(num_tasks):

We get the initial parameters of the model:

            old_w1, old_b1, old_w2, old_b2 = sess.run([w1, b1, w2, b2,])

Then, we sample x and y:

            x_sample, y_sample = sample_points(num_samples)

For some k number of iterations, we perform optimization on the task:

            for k in range(num_iterations):

                #get the minibatch x and y
                for i in range(0, num_samples, mini_batch):

                    #sample mini batch of examples 
                    x_minibatch = x_sample[i:i+mini_batch]
                    y_minibatch = y_sample[i:i+mini_batch]


                    train = sess.run(optimizer, feed_dict={X: x_minibatch.reshape(mini_batch,1), 
                                                           Y: y_minibatch.reshape(mini_batch,1)})

We get the updated model parameters after several iterations of optimization:

            new_w1, new_b1, new_w2, new_b2 = sess.run([w1, b1, w2, b2])

Now, we perform the meta update:

            epsilon = 0.1

            updated_w1 = old_w1 + epsilon * (new_w1 - old_w1) 
            updated_b1 = old_b1 + epsilon * (new_b1 - old_b1) 

            updated_w2 = old_w2 + epsilon * (new_w2 - old_w2) 
            updated_b2 = old_b2 + epsilon * (new_b2 - old_b2) 

We update the model parameter with new parameters:

            w1.load(updated_w1, sess)
            b1.load(updated_b1, sess)

            w2.load(updated_w2, sess)
            b2.load(updated_b2, sess)

Then, we print the loss for every 10 epochs:

        if e%10 == 0:
            loss = sess.run(loss_function, feed_dict={X: x_sample.reshape(num_samples,1), Y: y_sample.reshape(num_samples,1)})

            print "Epoch {}: Loss {}
".format(e,loss) 
            print 'Updated Model Parameter Theta
'
            print 'Sampling Next Batch of Tasks 
'
            print '---------------------------------
'

The complete code is given as follows:

#start the tensorflow session
with tf.Session() as sess:
    
    sess.run(init)
    
    for e in range(num_epochs):
        
        #for each task in batch of tasks
        for task in range(num_tasks):

            #get the initial parameters of the model
            old_w1, old_b1, old_w2, old_b2 = sess.run([w1, b1, w2, b2,])

            #sample x and y
            x_sample, y_sample = sample_points(num_samples)


            #for some k number of iterations perform optimization on the task
            for k in range(num_iterations):

                #get the minibatch x and y
                for i in range(0, num_samples, mini_batch):

                    #sample mini batch of examples 
                    x_minibatch = x_sample[i:i+mini_batch]
                    y_minibatch = y_sample[i:i+mini_batch]


                    train = sess.run(optimizer, feed_dict={X: x_minibatch.reshape(mini_batch,1), 
                                                           Y: y_minibatch.reshape(mini_batch,1)})

            #get the updated model parameters after several iterations of optimization
            new_w1, new_b1, new_w2, new_b2 = sess.run([w1, b1, w2, b2])

            #Now we perform meta update

            #i.e theta = theta + epsilon * (theta_star - theta)

            epsilon = 0.1

            updated_w1 = old_w1 + epsilon * (new_w1 - old_w1) 
            updated_b1 = old_b1 + epsilon * (new_b1 - old_b1) 

            updated_w2 = old_w2 + epsilon * (new_w2 - old_w2) 
            updated_b2 = old_b2 + epsilon * (new_b2 - old_b2) 


            #update the model parameter with new parameters
            w1.load(updated_w1, sess)
            b1.load(updated_b1, sess)

            w2.load(updated_w2, sess)
            b2.load(updated_b2, sess)

        if e%10 == 0:
            loss = sess.run(loss_function, feed_dict={X: x_sample.reshape(num_samples,1), Y: y_sample.reshape(num_samples,1)})

            print "Epoch {}: Loss {}
".format(e,loss) 
            print 'Updated Model Parameter Theta
'
            print 'Sampling Next Batch of Tasks 
'
            print '---------------------------------
'

You can see the output as follows:

Epoch 0: Loss 13.0675544739

Updated Model Parameter Theta

Sampling Next Batch of Tasks 

---------------------------------

Epoch 10: Loss 7.3604927063

Updated Model Parameter Theta

Sampling Next Batch of Tasks 

---------------------------------

Epoch 20: Loss 4.35141277313

Updated Model Parameter Theta

Sampling Next Batch of Tasks 

---------------------------------