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I'm trying to get the gradient of a function at two different values of the independent variable. I am doing this in the context of modifying the get_updates method of Keras' optimizer class.

The relevant section of the code I've written is

def get_updates(self, loss, params):
 grads = self.get_gradients(loss, params)
 self.updates = [K.update_add(self.iterations, 1)]

 # Copy parameters
 params2 = 
 for p in params:
 params2.append(K.variable(K.get_value(p), name=p.name[:-2] + "_cpy1/"))

 self.weights = [self.iterations]
 for p, p2, g in zip(params, params2, grads):
 v = - self.lr * g 
 new_p = p + 0.5*v # Intermediate/Partial step
 new_p2 = p2 + v # Reference point for 2nd Gradient

 grads2 = self.get_gradients(loss, params2)
 ....

The error I get when I execute this code is

 File "/home/me/Projects/RungeKutta/rk_optimizers2.py", line 86, in get_updates
 grads2 = self.get_gradients(loss, params2)
 File "/home/me/anaconda2/lib/python2.7/site-packages/keras/optimizers.py", line 91, in get_gradients
 raise ValueError('An operation has `None` for gradient. '
ValueError: An operation has `None` for gradient. Please make sure that all of your ops have a gradient defined (i.e. are differentiable). Common ops without gradient: K.argmax, K.round, K.eval.

The problematic section of code from Keras's optimizers.py is:

def get_gradients(self, loss, params):
 grads = K.gradients(loss, params)
 if None in grads:
 raise ValueError('An operation has `None` for gradient. '
 'Please make sure that all of your ops have a '
 'gradient defined (i.e. are differentiable). '
 'Common ops without gradient: '
 'K.argmax, K.round, K.eval.')

In my case, K corresponds to Tensorflow. So, the corresponding code for gradients is:

def gradients(loss, variables):
 """Returns the gradients of `loss` w.r.t. `variables`.

 # Arguments
 loss: Scalar tensor to minimize.
 variables: List of variables.

 # Returns
 A gradients tensor.
 """
 return tf.gradients(loss, variables, colocate_gradients_with_ops=True)

Why do I get the error I see? How can I get a gradient at the first projected updated parameter so that I can get a final update using the average of the gradient at the starting point and the gradient at an (initially) projected end point?