Neural network output issue - tensorflow

Question

I built a neural network with tensorflow, here the code :
class DQNetwork:
def __init__(self, state_size, action_size, learning_rate, name='DQNetwork'):
self.state_size = state_size
self.action_size = action_size
self.learning_rate = learning_rate
with tf.variable_scope(name):
# We create the placeholders
self.inputs_ = tf.placeholder(tf.float32, shape=[state_size[1], state_size[0]], name="inputs")
self.actions_ = tf.placeholder(tf.float32, [None, self.action_size], name="actions_")
# Remember that target_Q is the R(s,a) + ymax Qhat(s', a')
self.target_Q = tf.placeholder(tf.float32, [None], name="target")
self.fc = tf.layers.dense(inputs = self.inputs_,
units = 50,
kernel_initializer=tf.contrib.layers.xavier_initializer(),
activation = tf.nn.elu)
self.output = tf.layers.dense(inputs = self.fc,
units = self.action_size,
kernel_initializer=tf.contrib.layers.xavier_initializer(),
activation=None)
# Q is our predicted Q value.
self.Q = tf.reduce_sum(tf.multiply(self.output, self.actions_))
# The loss is the difference between our predicted Q_values and the Q_target
# Sum(Qtarget - Q)^2
self.loss = tf.reduce_mean(tf.square(self.target_Q - self.Q))
self.optimizer = tf.train.AdamOptimizer(self.learning_rate).minimize(self.loss)
But i have an issue with the output,
the output should normaly be at the same size than "action_size", and action_size value is 3
but i got an output like [[5][3]] instead of just [[3]] and i realy don't understand why...
This network got 2 dense layers, one with 50 perceptrons and the other with 3 perceptrons (= action_size).
state_size is format : [[9][5]]
If someone know why my output is two dimensions i will be very thankful

Answer 1

Your self.inputs_ placeholder has shape (5, 9). You perform the matmul(self.inputs_, fc1.w) operation in dense layer fc1 which has shape (9, 50) and it results in shape (5, 50). You then apply another dense layer with shape (50, 3) which results in output shape (5, 3).
The same schematically:
matmul(shape(5, 9), shape(9, 50)) ---> shape(5, 50) # output of 1st dense layer
matmul(shape(5, 50), shape(50, 3)) ---> shape(5, 3) # output of 2nd dense layer
Usually, the first dimension of the input placeholder represents batch size and the second dimension is the dimension of inputs feature vector. So for each sample in a batch you (batch size is 5 in your case) you get the output shape 3.
To get probabilities, use this:
import tensorflow as tf
import numpy as np
inputs_ = tf.placeholder(tf.float32, shape=(None, 9))
actions_ = tf.placeholder(tf.float32, shape=(None, 3))
fc = tf.layers.dense(inputs=inputs_, units=2)
output = tf.layers.dense(inputs=fc, units=3)
reduced = tf.reduce_mean(output, axis=0)
probs = tf.nn.softmax(reduced) # <--probabilities
inputs_vals = np.ones((5, 9))
actions_vals = np.ones((1, 3))
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
print(probs.eval({inputs_:inputs_vals,
actions_:actions_vals}))
# [0.01858923 0.01566187 0.9657489 ]