external_optimizer.py
# pylint: skip-file
#
# Copyright 2016 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.
# ==============================================================================
"""TensorFlow interface for third-party optimizers."""
from __future__ import absolute_import, division, print_function
import numpy as np
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops, gradients, variables
from tensorflow.python.platform import tf_logging as logging
__all__ = ['ExternalOptimizerInterface', 'ScipyOptimizerInterface']
class ExternalOptimizerInterface(object):
"""Base class for interfaces with external optimization algorithms.
Subclass this and implement `_minimize` in order to wrap a new optimization
algorithm.
`ExternalOptimizerInterface` should not be instantiated directly; instead use
e.g. `ScipyOptimizerInterface`.
@@__init__
@@minimize
"""
def __init__(self, loss, var_list=None, equalities=None, inequalities=None, var_to_bounds=None,
**optimizer_kwargs):
"""Initialize a new interface instance.
Args:
loss: A scalar `Tensor` to be minimized.
var_list: Optional `list` of `Variable` objects to update to minimize
`loss`. Defaults to the list of variables collected in the graph
under the key `GraphKeys.TRAINABLE_VARIABLES`.
equalities: Optional `list` of equality constraint scalar `Tensor`s to be
held equal to zero.
inequalities: Optional `list` of inequality constraint scalar `Tensor`s
to be held nonnegative.
var_to_bounds: Optional `dict` where each key is an optimization
`Variable` and each corresponding value is a length-2 tuple of
`(low, high)` bounds. Although enforcing this kind of simple constraint
could be accomplished with the `inequalities` arg, not all optimization
algorithms support general inequality constraints, e.g. L-BFGS-B. Both
`low` and `high` can either be numbers or anything convertible to a
NumPy array that can be broadcast to the shape of `var` (using
`np.broadcast_to`). To indicate that there is no bound, use `None` (or
`+/- np.infty`). For example, if `var` is a 2x3 matrix, then any of
the following corresponding `bounds` could be supplied:
* `(0, np.infty)`: Each element of `var` held positive.
* `(-np.infty, [1, 2])`: First column less than 1, second column less
than 2.
* `(-np.infty, [[1], [2], [3]])`: First row less than 1, second row less
than 2, etc.
* `(-np.infty, [[1, 2, 3], [4, 5, 6]])`: Entry `var[0, 0]` less than 1,
`var[0, 1]` less than 2, etc.
**optimizer_kwargs: Other subclass-specific keyword arguments.
"""
self.optimizer_kwargs = optimizer_kwargs
self._loss = loss
self._equalities = equalities or []
self._inequalities = inequalities or []
self._var_to_bounds = var_to_bounds
if var_list is None:
self._vars = variables.trainable_variables()
elif var_list == []:
raise ValueError("No variables to optimize.")
else:
self._vars = list(var_list)
self._packed_bounds = []
self._update_placeholders = []
self._var_updates = []
self._packed_var = None
self._packed_loss_grad = None
self._packed_equality_grads = []
self._packed_inequality_grads = []
self._var_shapes = None
self._feed_dict = None
def minimize(self,
session=None,
feed_dict=None,
fetches=None,
step_callback=None,
loss_callback=None,
**optimizer_kwargs):
"""Minimize a scalar `Tensor`.
Variables subject to optimization are updated in-place at the end of
optimization.
Note that this method does *not* just return a minimization `Op`, unlike
`Optimizer.minimize()`; instead it actually performs minimization by
executing commands to control a `Session`.
Args:
session: A `Session` instance.
feed_dict: A feed dict to be passed to calls to `session.run`.
fetches: A list of `Tensor`s to fetch and supply to `loss_callback`
as positional arguments.
step_callback: A function to be called at each optimization step;
arguments are the current values of all optimization variables
flattened into a single vector.
loss_callback: A function to be called every time the loss and gradients
are computed, with evaluated fetches supplied as positional arguments.
**optimizer_kwargs: kwargs to pass to ScipyOptimizer `minimize` method.
"""
session = session or ops.get_default_session()
self.init_optimize(session=session, fetches=fetches, loss_callback=loss_callback, **optimizer_kwargs)
self.optimize(session=session, step_callback=step_callback, feed_dict=feed_dict)
def init_optimize(self, session=None, fetches=None, loss_callback=None, **optimizer_kwargs):
"""Create intermediate tensors for optimizing a scalar `Tensor`.
Variables subject to optimization are updated in-place at the end of
optimization.
Note that this method does *not* just return a minimization `Op`, unlike
`Optimizer.minimize()`; instead it actually performs minimization by
executing commands to control a `Session`.
Args:
session: A `Session` instance.
feed_dict: A feed dict to be passed to calls to `session.run`.
fetches: A list of `Tensor`s to fetch and supply to `loss_callback`
as positional arguments.
step_callback: A function to be called at each optimization step;
arguments are the current values of all optimization variables
flattened into a single vector.
loss_callback: A function to be called every time the loss and gradients
are computed, with evaluated fetches supplied as positional arguments.
**optimizer_kwargs: kwargs to pass to ScipyOptimizer `minimize` method.
"""
session = session or ops.get_default_session()
fetches = fetches or []
loss_callback = loss_callback or (lambda *fetches: None)
# Get initial value from TF session.
self._initialize_updated_shapes(session)
self._make_minimize_tensors(session, fetches, loss_callback, **optimizer_kwargs)
def optimize(self, session=None, step_callback=None, feed_dict=None):
"""
Runs optimization on a scalar `Tensor` defined by `init_optimize`.
Args:
**run_kwargs: kwargs to pass to `session.run`.
"""
session = session or ops.get_default_session()
step_callback = step_callback or (lambda xk: None)
# Perform minimization.
self._feed_dict = feed_dict if feed_dict is not None else {}
initial_packed_var_val = session.run(self._packed_var)
packed_var_val = self._minimize(initial_val=initial_packed_var_val,
packed_bounds=self._packed_bounds,
optimizer_kwargs=self.optimizer_kwargs,
step_callback=step_callback,
**self._minimize_args)
var_vals = [packed_var_val[packing_slice] for packing_slice in self._packing_slices]
# Set optimization variables to their new values.
run_feed_dict = dict(zip(self._update_placeholders, var_vals))
session.run(self._var_updates, feed_dict=run_feed_dict)
def _make_minimize_tensors(self, session, fetches, callback, **optimizer_kwargs):
# Construct loss function and associated gradient.
loss_grad_func = self._make_eval_func([self._loss, self._packed_loss_grad], session, fetches, callback)
# Construct equality constraint functions and associated gradients.
equality_funcs = self._make_eval_funcs(self._equalities, session, fetches)
equality_grad_funcs = self._make_eval_funcs(self._packed_equality_grads, session, fetches)
# Construct inequality constraint functions and associated gradients.
inequality_funcs = self._make_eval_funcs(self._inequalities, session, fetches)
inequality_grad_funcs = self._make_eval_funcs(self._packed_inequality_grads, session, fetches)
kwargs = dict(loss_grad_func=loss_grad_func,
equality_funcs=equality_funcs,
equality_grad_funcs=equality_grad_funcs,
inequality_funcs=inequality_funcs,
inequality_grad_funcs=inequality_grad_funcs)
kwargs.update(optimizer_kwargs)
self._minimize_args = kwargs
def _initialize_updated_shapes(self, session):
shapes = array_ops.shape_n(self._vars)
var_shapes = list(map(tuple, session.run(shapes)))
if self._var_shapes is not None:
new_old_shapes = zip(self._var_shapes, var_shapes)
if all([old == new for old, new in new_old_shapes]):
return
self._var_shapes = var_shapes
vars_and_shapes = zip(self._vars, self._var_shapes)
vars_and_shapes_dict = dict(vars_and_shapes)
packed_bounds = None
if self._var_to_bounds is not None:
left_packed_bounds = []
right_packed_bounds = []
for var, var_shape in vars_and_shapes:
shape = list(var_shape)
bounds = (-np.infty, np.infty)
if var in var_to_bounds:
bounds = var_to_bounds[var]
left_packed_bounds.extend(list(np.broadcast_to(bounds[0], shape).flat))
right_packed_bounds.extend(list(np.broadcast_to(bounds[1], shape).flat))
packed_bounds = list(zip(left_packed_bounds, right_packed_bounds))
self._packed_bounds = packed_bounds
self._update_placeholders = [array_ops.placeholder(var.dtype) for var in self._vars]
self._var_updates = [
var.assign(array_ops.reshape(placeholder, vars_and_shapes_dict[var]))
for var, placeholder in zip(self._vars, self._update_placeholders)
]
loss_grads = _compute_gradients(self._loss, self._vars)
equalities_grads = [_compute_gradients(equality, self._vars) for equality in self._equalities]
inequalities_grads = [_compute_gradients(inequality, self._vars) for inequality in self._inequalities]
self._packed_var = self._pack(self._vars)
self._packed_loss_grad = self._pack(loss_grads)
self._packed_equality_grads = [self._pack(equality_grads) for equality_grads in equalities_grads]
self._packed_inequality_grads = [self._pack(inequality_grads) for inequality_grads in inequalities_grads]
dims = [_prod(vars_and_shapes_dict[var]) for var in self._vars]
accumulated_dims = list(_accumulate(dims))
self._packing_slices = [slice(start, end) for start, end in zip(accumulated_dims[:-1], accumulated_dims[1:])]
def _minimize(self, initial_val, loss_grad_func, equality_funcs, equality_grad_funcs, inequality_funcs,
inequality_grad_funcs, packed_bounds, step_callback, optimizer_kwargs):
"""Wrapper for a particular optimization algorithm implementation.
It would be appropriate for a subclass implementation of this method to
raise `NotImplementedError` if unsupported arguments are passed: e.g. if an
algorithm does not support constraints but `len(equality_funcs) > 0`.
Args:
initial_val: A NumPy vector of initial values.
loss_grad_func: A function accepting a NumPy packed variable vector and
returning two outputs, a loss value and the gradient of that loss with
respect to the packed variable vector.
equality_funcs: A list of functions each of which specifies a scalar
quantity that an optimizer should hold exactly zero.
equality_grad_funcs: A list of gradients of equality_funcs.
inequality_funcs: A list of functions each of which specifies a scalar
quantity that an optimizer should hold >= 0.
inequality_grad_funcs: A list of gradients of inequality_funcs.
packed_bounds: A list of bounds for each index, or `None`.
step_callback: A callback function to execute at each optimization step,
supplied with the current value of the packed variable vector.
optimizer_kwargs: Other key-value arguments available to the optimizer.
Returns:
The optimal variable vector as a NumPy vector.
"""
raise NotImplementedError('To use ExternalOptimizerInterface, subclass from it and implement '
'the _minimize() method.')
@classmethod
def _pack(cls, tensors):
"""Pack a list of `Tensor`s into a single, flattened, rank-1 `Tensor`."""
if not tensors:
return None
elif len(tensors) == 1:
return array_ops.reshape(tensors[0], [-1])
else:
flattened = [array_ops.reshape(tensor, [-1]) for tensor in tensors]
return array_ops.concat(flattened, 0)
def _make_eval_func(self, tensors, session, fetches, callback=None):
"""Construct a function that evaluates a `Tensor` or list of `Tensor`s."""
if not isinstance(tensors, list):
tensors = [tensors]
num_tensors = len(tensors)
def eval_func(x):
"""Function to evaluate a `Tensor`."""
shapes = dict(zip(self._vars, self._var_shapes))
augmented_feed_dict = {
var: x[packing_slice].reshape(shapes[var])
for var, packing_slice in zip(self._vars, self._packing_slices)
}
augmented_feed_dict.update(self._feed_dict)
augmented_fetches = tensors + fetches
augmented_fetch_vals = session.run(augmented_fetches, feed_dict=augmented_feed_dict)
if callable(callback):
callback(*augmented_fetch_vals[num_tensors:])
return augmented_fetch_vals[:num_tensors]
return eval_func
def _make_eval_funcs(self, tensors, session, fetches, callback=None):
return [self._make_eval_func(tensor, session, fetches, callback) for tensor in tensors]
class ScipyOptimizerInterface(ExternalOptimizerInterface):
"""Wrapper allowing `scipy.optimize.minimize` to operate a `tf.Session`.
Example:
```python
vector = tf.Variable([7., 7.], 'vector')
# Make vector norm as small as possible.
loss = tf.reduce_sum(tf.square(vector))
optimizer = ScipyOptimizerInterface(loss, options={'maxiter': 100})
with tf.Session() as session:
optimizer.minimize(session)
# The value of vector should now be [0., 0.].
```
Example with simple bound constraints:
```python
vector = tf.Variable([7., 7.], 'vector')
# Make vector norm as small as possible.
loss = tf.reduce_sum(tf.square(vector))
optimizer = ScipyOptimizerInterface(
loss, var_to_bounds={vector: ([1, 2], np.infty)})
with tf.Session() as session:
optimizer.minimize(session)
# The value of vector should now be [1., 2.].
```
Example with more complicated constraints:
```python
vector = tf.Variable([7., 7.], 'vector')
# Make vector norm as small as possible.
loss = tf.reduce_sum(tf.square(vector))
# Ensure the vector's y component is = 1.
equalities = [vector[1] - 1.]
# Ensure the vector's x component is >= 1.
inequalities = [vector[0] - 1.]
# Our default SciPy optimization algorithm, L-BFGS-B, does not support
# general constraints. Thus we use SLSQP instead.
optimizer = ScipyOptimizerInterface(
loss, equalities=equalities, inequalities=inequalities, method='SLSQP')
with tf.Session() as session:
optimizer.minimize(session)
# The value of vector should now be [1., 1.].
```
"""
_DEFAULT_METHOD = 'L-BFGS-B'
def _minimize(self, initial_val, loss_grad_func, equality_funcs, equality_grad_funcs, inequality_funcs,
inequality_grad_funcs, packed_bounds, step_callback, optimizer_kwargs):
def loss_grad_func_wrapper(x):
# SciPy's L-BFGS-B Fortran implementation requires gradients as doubles.
loss, gradient = loss_grad_func(x)
return loss, gradient.astype('float64')
method = optimizer_kwargs.pop('method', self._DEFAULT_METHOD)
constraints = []
for func, grad_func in zip(equality_funcs, equality_grad_funcs):
constraints.append({'type': 'eq', 'fun': func, 'jac': grad_func})
for func, grad_func in zip(inequality_funcs, inequality_grad_funcs):
constraints.append({'type': 'ineq', 'fun': func, 'jac': grad_func})
minimize_args = [loss_grad_func_wrapper, initial_val]
minimize_kwargs = {
'jac': True,
'callback': step_callback,
'method': method,
'constraints': constraints,
'bounds': packed_bounds,
}
for kwarg in minimize_kwargs:
if kwarg in optimizer_kwargs:
if kwarg == 'bounds':
# Special handling for 'bounds' kwarg since ability to specify bounds
# was added after this module was already publicly released.
raise ValueError('Bounds must be set using the var_to_bounds argument')
raise ValueError('Optimizer keyword arg \'{}\' is set '
'automatically and cannot be injected manually'.format(kwarg))
minimize_kwargs.update(optimizer_kwargs)
if method == 'SLSQP':
# SLSQP doesn't support step callbacks. Obviate associated warning
# message.
del minimize_kwargs['callback']
import scipy.optimize # pylint: disable=g-import-not-at-top
result = scipy.optimize.minimize(*minimize_args, **minimize_kwargs)
logging.info(
'Optimization terminated with:\n'
' Message: %s\n'
' Objective function value: %f\n'
' Number of iterations: %d\n'
' Number of functions evaluations: %d', result.message, result.fun, result.nit, result.nfev)
return result['x']
def _accumulate(list_):
total = 0
yield total
for x in list_:
total += x
yield total
def _prod(array):
prod = 1
for value in array:
prod *= value
return prod
def _compute_gradients(tensor, var_list):
grads = gradients.gradients(tensor, var_list)
# tf.gradients sometimes returns `None` when it should return 0.
return [grad if grad is not None else array_ops.zeros_like(var) for var, grad in zip(var_list, grads)]
