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# Copyright 2017 The TensorFlow Authors All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Trust region optimization.
A lot of this is adapted from other's code.
See Schulman's Modular RL, wojzaremba's TRPO, etc.
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from six.moves import xrange
import tensorflow as tf
import numpy as np
def var_size(v):
return int(np.prod([int(d) for d in v.shape]))
def gradients(loss, var_list):
grads = tf.gradients(loss, var_list)
return [g if g is not None else tf.zeros(v.shape)
for g, v in zip(grads, var_list)]
def flatgrad(loss, var_list):
grads = gradients(loss, var_list)
return tf.concat([tf.reshape(grad, [-1])
for (v, grad) in zip(var_list, grads)
if grad is not None], 0)
def get_flat(var_list):
return tf.concat([tf.reshape(v, [-1]) for v in var_list], 0)
def set_from_flat(var_list, flat_theta):
assigns = []
shapes = [v.shape for v in var_list]
sizes = [var_size(v) for v in var_list]
start = 0
assigns = []
for (shape, size, v) in zip(shapes, sizes, var_list):
assigns.append(v.assign(
tf.reshape(flat_theta[start:start + size], shape)))
start += size
assert start == sum(sizes)
return tf.group(*assigns)
class TrustRegionOptimization(object):
def __init__(self, max_divergence=0.1, cg_damping=0.1):
self.max_divergence = max_divergence
self.cg_damping = cg_damping
def setup_placeholders(self):
self.flat_tangent = tf.placeholder(tf.float32, [None], 'flat_tangent')
self.flat_theta = tf.placeholder(tf.float32, [None], 'flat_theta')
def setup(self, var_list, raw_loss, self_divergence,
divergence=None):
self.setup_placeholders()
self.raw_loss = raw_loss
self.divergence = divergence
self.loss_flat_gradient = flatgrad(raw_loss, var_list)
self.divergence_gradient = gradients(self_divergence, var_list)
shapes = [var.shape for var in var_list]
sizes = [var_size(var) for var in var_list]
start = 0
tangents = []
for shape, size in zip(shapes, sizes):
param = tf.reshape(self.flat_tangent[start:start + size], shape)
tangents.append(param)
start += size
assert start == sum(sizes)
self.grad_vector_product = sum(
tf.reduce_sum(g * t) for (g, t) in zip(self.divergence_gradient, tangents))
self.fisher_vector_product = flatgrad(self.grad_vector_product, var_list)
self.flat_vars = get_flat(var_list)
self.set_vars = set_from_flat(var_list, self.flat_theta)
def optimize(self, sess, feed_dict):
old_theta = sess.run(self.flat_vars)
loss_flat_grad = sess.run(self.loss_flat_gradient,
feed_dict=feed_dict)
def calc_fisher_vector_product(tangent):
feed_dict[self.flat_tangent] = tangent
fvp = sess.run(self.fisher_vector_product,
feed_dict=feed_dict)
fvp += self.cg_damping * tangent
return fvp
step_dir = conjugate_gradient(calc_fisher_vector_product, -loss_flat_grad)
shs = 0.5 * step_dir.dot(calc_fisher_vector_product(step_dir))
lm = np.sqrt(shs / self.max_divergence)
fullstep = step_dir / lm
neggdotstepdir = -loss_flat_grad.dot(step_dir)
def calc_loss(theta):
sess.run(self.set_vars, feed_dict={self.flat_theta: theta})
if self.divergence is None:
return sess.run(self.raw_loss, feed_dict=feed_dict), True
else:
raw_loss, divergence = sess.run(
[self.raw_loss, self.divergence], feed_dict=feed_dict)
return raw_loss, divergence < self.max_divergence
# find optimal theta
theta = linesearch(calc_loss, old_theta, fullstep, neggdotstepdir / lm)
if self.divergence is not None:
final_divergence = sess.run(self.divergence, feed_dict=feed_dict)
else:
final_divergence = None
# set vars accordingly
if final_divergence is None or final_divergence < self.max_divergence:
sess.run(self.set_vars, feed_dict={self.flat_theta: theta})
else:
sess.run(self.set_vars, feed_dict={self.flat_theta: old_theta})
def conjugate_gradient(f_Ax, b, cg_iters=10, residual_tol=1e-10):
p = b.copy()
r = b.copy()
x = np.zeros_like(b)
rdotr = r.dot(r)
for i in xrange(cg_iters):
z = f_Ax(p)
v = rdotr / p.dot(z)
x += v * p
r -= v * z
newrdotr = r.dot(r)
mu = newrdotr / rdotr
p = r + mu * p
rdotr = newrdotr
if rdotr < residual_tol:
break
return x
def linesearch(f, x, fullstep, expected_improve_rate):
accept_ratio = 0.1
max_backtracks = 10
fval, _ = f(x)
for (_n_backtracks, stepfrac) in enumerate(.5 ** np.arange(max_backtracks)):
xnew = x + stepfrac * fullstep
newfval, valid = f(xnew)
if not valid:
continue
actual_improve = fval - newfval
expected_improve = expected_improve_rate * stepfrac
ratio = actual_improve / expected_improve
if ratio > accept_ratio and actual_improve > 0:
return xnew
return x
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