Use theano to do binary search over continuous monotonic increasing function

theano_binary_search.py

# Use theano to do binary search over continuous monotonic increasing function

import theano
import theano.tensor as T

import numpy as np


def func(x):
    return T.exp(x)

magnify = 2.

xmin_init = 1e-16
xmax_init = np.inf
x_init = 1.
y_target = 100.

x = T.scalar()
y = T.scalar()
xmin = T.scalar()
xmax = T.scalar()

x_shared = theano.shared(x_init)
xmin_shared = theano.shared(xmin_init)
xmax_shared = theano.shared(xmax_init)


new_xmin = T.switch(T.lt(func(x), y), x, xmin)
new_xmax = T.switch(T.gt(func(x), y), x, xmax)
new_x = T.switch(T.isinf(new_xmax), magnify * x, (new_xmax + new_xmin) / 2.)

givens = [(x, x_shared), (xmin, xmin_shared), (xmax, xmax_shared)]
updates = [(x_shared, new_x), (xmin_shared, new_xmin), (xmax_shared, new_xmax)]

run_update = theano.function([y], func(x), givens=givens, updates=updates)


for ii in range(20):
    print "y:", run_update(y_target), "x:", x_shared.get_value()