Tensorflow minimise with respect to only some elements of a variable

I'm not sure if it is possible with the SciPy optimizer interface, but using one of the regular tf.train.Optimizer subclasses you can do something like that by calling compute_gradients first, then masking the gradients and then calling apply_gradients, instead of calling minimize (which, as the docs say, basically calls the previous ones).

import tensorflow as tf

X = tf.Variable([3.0, 2.0])
# Select updatable parameters
X_mask = tf.constant([True, False], dtype=tf.bool)
Y = tf.constant([2.0, -3.0])
loss = tf.reduce_sum(tf.squared_difference(X, Y))
opt = tf.train.GradientDescentOptimizer(learning_rate=0.1)
# Get gradients and mask them
((X_grad, _),) = opt.compute_gradients(loss, var_list=[X])
X_grad_masked = X_grad * tf.cast(X_mask, dtype=X_grad.dtype)
# Apply masked gradients
train_step = opt.apply_gradients([(X_grad_masked, X)])

init = tf.global_variables_initializer()
with tf.Session() as sess:
    sess.run(init)
    for i in range(10):
        _, X_val = sess.run([train_step, X])
        print("Step {}: X = {}".format(i, X_val))
    print("Final X = {}".format(X.eval()))

Output:

Step 0: X = [ 2.79999995  2.        ]
Step 1: X = [ 2.63999987  2.        ]
Step 2: X = [ 2.51199985  2.        ]
Step 3: X = [ 2.40959978  2.        ]
Step 4: X = [ 2.32767987  2.        ]
Step 5: X = [ 2.26214385  2.        ]
Step 6: X = [ 2.20971513  2.        ]
Step 7: X = [ 2.16777205  2.        ]
Step 8: X = [ 2.13421774  2.        ]
Step 9: X = [ 2.10737419  2.        ]
Final X = [ 2.10737419  2.        ]

You can use this trick to restrict the gradient calculation to one index:

import tensorflow as tf
import tensorflow.contrib.opt as opt

X = tf.Variable([1.0, 2.0])

part_X = tf.scatter_nd([[0]], [X[0]], [2])

X_2 = part_X + tf.stop_gradient(-part_X + X)

Y = tf.constant([2.0, -3.0])

loss = tf.reduce_sum(tf.squared_difference(X_2, Y))

opt = opt.ScipyOptimizerInterface(loss, [X])

init = tf.global_variables_initializer()

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

    print("X: {}".format(X.eval()))

part_X becomes the value you want to change in a one-hot vector of the same shape as X. part_X + tf.stop_gradient(-part_X + X) is the same as X in the forward pass, since part_X - part_X is 0. However in the backward pass the tf.stop_gradient prevents all unnecessary gradient calculations.

This should be pretty easy to do by using the var_list parameter of the minimize function.

trainable_var = X[0]
train_op = tf.train.GradientDescentOptimizer(learning_rate=1e-3).minimize(loss, var_list=[trainable_var])

You should note that by convention all trainable variables are added to the tensorflow default collection GraphKeys.TRAINABLE_VARIABLES, so you can get a list of all trainable variables using:

all_trainable_vars = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES)

This is just a list of variables which you can manipulate as you see fit and use as the var_list parameter.

As a tangent to your question, if you ever want to take customizing the optimization process a step further you can also compute the gradients manually using grads = tf.gradients(loss, var_list) manipulate the gradients as you see fit, then call tf.train.GradientDescentOptimizer(...).apply_gradients(grads_and_vars_as_list_of_tuples). Under the hood minimize is just doing these two steps for you.

Also note that you are perfectly free to create different optimizers for different collections of variables. You could create an SGD optimizer with learning rate 1e-4 for some variables, and another Adam optimizer with learning rate 1e-2 for another set of variables. Not that there's any specific use case for this, I'm just pointing out the flexibility you now have.