python - Tensorflow Linear Regression - Exponential Model Not Fitting Exponent -

i'm trying fit exponentially decaying model (y=ax^b + c)to data have yet value other 0 for b. have 2 "working" sets of code right now, 1 steps through each x,y pair, , other attempts use entire [x,y] array, i'm not sure have implemented correctly. i'd correctly fit curve. linear model works fine i'm not sure going south.

data here - pastebin

#!/usr/bin/python  import numpy np import tensorflow tf import sys import matplotlib.pyplot plt k=0 xdata= [] ydata = [] # open data , read in, ignore header. open('curvedata_full_formatted.csv') f:     line in f:         k+=1         if k==1:continue         items = line.split(',')         xdata.append(float(items[0]))         ydata.append(float(items[1]))   # model linear regression y = a*x^b+c # x - data fed model - 1 feature x = tf.placeholder(tf.float32, [none, 1])  # - training variable - 1 feature, 1 output = tf.variable(tf.zeros([1,1]))  # b - training variable - 1 output b = tf.variable(tf.zeros([1,1]))  # c - training variable - 1 output c = tf.variable(tf.zeros([1]))  # x^b xb = tf.exp(b) # a*x^b product = tf.mul(a,xb)   # prediction y = tf.add(product,c) # actual value ybar  y_ = tf.placeholder(tf.float32) # cost function sum((y_-y)**2) cost = tf.reduce_mean(tf.square(y_-y))  # training using gradient descent minimize cost train_step = tf.train.gradientdescentoptimizer(1*10**-9).minimize(cost)  sess = tf.session() init = tf.initialize_all_variables() sess.run(init) steps = 150  in range(steps):     # read in data log file , use x,y     (x,y) in zip(xdata,ydata):         #xs = np.array([[xdata]])         #ys = np.array([[ydata]])         # train         # feed dict x placeholder xs, y_ placeholder ys         x = np.array([[x]])         y = np.array([[y]])         feed = { x: x, y_: y }         sess.run(train_step, feed_dict=feed)     sys.stdout.write("\riteration %i " %i +"cost %.15f" % sess.run(cost,     feed_dict=feed))     sys.stdout.flush() print '' print 'a: %f'%sess.run(a) print 'b: %f'%sess.run(b) print 'c: %f'%sess.run(c)    

as test, try starting optimizer initial values close expected final parameters. test tell whether or not problem in selection of initial parameter values.