def testGroup_MultiDevice(self):
with ops.Graph().as_default() as g:
with g.device("/task:0"):
a = tf.constant(0, name="a")
b = tf.constant(0, name="b")
with g.device("/task:1"):
c = tf.constant(0, name="c")
d = tf.constant(0, name="d")
with g.device("/task:2"):
tf.group(a.op, b.op, c.op, d.op, name="root")
gd = g.as_graph_def()
self.assertProtoEquals(
"""
node { name: "a" op: "Const" device: "/task:0"}
node { name: "b" op: "Const" device: "/task:0"}
node { name: "c" op: "Const" device: "/task:1"}
node { name: "d" op: "Const" device: "/task:1"}
node { name: "root/NoOp" op: "NoOp" input: "^a" input: "^b"
device: "/task:0" }
node { name: "root/NoOp_1" op: "NoOp" input: "^c" input: "^d"
device: "/task:1" }
node { name: "root" op: "NoOp" input: "^root/NoOp" input: "^root/NoOp_1"
device: "/task:2" }
""",
self._StripGraph(gd),
)
def testIndexedSlicesGradientInCondInWhileLoop(self):
with ops.Graph().as_default():
embedding_matrix = tf.get_variable(
"embedding_matrix", [5, 5],
initializer=tf.random_normal_initializer())
def Cond(it, _):
return it < 5
def Body(it, cost):
embedding = embedding_ops.embedding_lookup(embedding_matrix, [0])
cost = tf.cond(tf.equal(it, 3),
lambda: tf.square(cost),
lambda: cost + tf.reduce_sum(embedding))
return it + 1, cost
_, cost = control_flow_ops.While(
Cond, Body, [tf.constant(0), tf.constant(0.0)])
dynamic_grads = tf.gradients(cost, [embedding_matrix])[0]
dynamic_grads = tf.segment_sum(dynamic_grads.values,
dynamic_grads.indices)
embedding = embedding_ops.embedding_lookup(embedding_matrix, [0])
static = tf.square(
tf.reduce_sum(embedding) +
tf.reduce_sum(embedding) +
tf.reduce_sum(embedding)) + tf.reduce_sum(embedding)
static_grads = tf.gradients(static, [embedding_matrix])[0]
static_grads = tf.segment_sum(static_grads.values, static_grads.indices)
with self.test_session() as sess:
sess.run(tf.initialize_all_variables())
self.assertAllEqual(*sess.run([static_grads, dynamic_grads]))
def test_maximum_eigenvector_power_method(self):
"""Tests power method routine on some known left-stochastic matrices."""
matrix1 = np.matrix([[0.6, 0.1, 0.1], [0.0, 0.6, 0.9], [0.4, 0.3,
0.0]])
matrix2 = np.matrix([[0.4, 0.4, 0.2], [0.2, 0.1, 0.5], [0.4, 0.5,
0.3]])
with self.cached_session() as session:
eigenvector1 = session.run(
swap_regret_optimizer._maximal_eigenvector_power_method(
standard_ops.constant(matrix1)))
eigenvector2 = session.run(
swap_regret_optimizer._maximal_eigenvector_power_method(
standard_ops.constant(matrix2)))
# Check that eigenvector1 and eigenvector2 are eigenvectors of matrix1 and
# matrix2 (respectively) with associated eigenvalue 1.
matrix_eigenvector1 = np.tensordot(matrix1, eigenvector1, axes=1)
matrix_eigenvector2 = np.tensordot(matrix2, eigenvector2, axes=1)
self.assertAllClose(eigenvector1,
matrix_eigenvector1,
rtol=0,
atol=1e-6)
self.assertAllClose(eigenvector2,
matrix_eigenvector2,
rtol=0,
atol=1e-6)
def test_project_multipliers_wrt_euclidean_norm(self):
"""Tests Euclidean projection routine on some known values."""
multipliers1 = standard_ops.constant([-0.1, -0.6, -0.3])
expected_projected_multipliers1 = np.array([0.0, 0.0, 0.0])
multipliers2 = standard_ops.constant([-0.1, 0.6, 0.3])
expected_projected_multipliers2 = np.array([0.0, 0.6, 0.3])
multipliers3 = standard_ops.constant([0.4, 0.7, -0.2, 0.5, 0.1])
expected_projected_multipliers3 = np.array([0.2, 0.5, 0.0, 0.3, 0.0])
with self.test_session() as session:
projected_multipliers1 = session.run(
external_regret_optimizer.
_project_multipliers_wrt_euclidean_norm(multipliers1, 1.0))
projected_multipliers2 = session.run(
external_regret_optimizer.
_project_multipliers_wrt_euclidean_norm(multipliers2, 1.0))
projected_multipliers3 = session.run(
external_regret_optimizer.
_project_multipliers_wrt_euclidean_norm(multipliers3, 1.0))
self.assertAllClose(expected_projected_multipliers1,
projected_multipliers1,
rtol=0,
atol=1e-6)
self.assertAllClose(expected_projected_multipliers2,
projected_multipliers2,
rtol=0,
atol=1e-6)
self.assertAllClose(expected_projected_multipliers3,
projected_multipliers3,
rtol=0,
atol=1e-6)
def testShape(self):
with ops.Graph().as_default():
tensor = tf.constant([1.0, 2.0])
self.assertEquals([2], tensor.get_shape())
self.assertEquals([2],
control_flow_ops.with_dependencies(
[tf.constant(1.0)], tensor).get_shape())
def testIndexedSlicesWithDenseShape(self):
with self.test_session():
data = ops.IndexedSlices(tf.constant([1, 2, 3]), tf.constant([0, 1]), dense_shape=tf.constant([3]))
zero = tf.constant(0)
one = tf.constant(1)
less_op = tf.less(zero, one)
switch_false, switch_true = control_flow_ops.switch(data, less_op)
self.assertAllEqual([1, 2, 3], switch_true.values.eval())
self.assertAllEqual([0, 1], switch_true.indices.eval())
def testIndexedSlicesWithDenseShape(self):
with self.test_session():
data = ops.IndexedSlices(tf.constant([1, 2, 3]),
tf.constant([0, 1]),
dense_shape=tf.constant([3]))
zero = tf.constant(0)
one = tf.constant(1)
less_op = tf.less(zero, one)
switch_false, switch_true = control_flow_ops.switch(data, less_op)
self.assertAllEqual([1, 2, 3], switch_true.values.eval())
self.assertAllEqual([0, 1], switch_true.indices.eval())
def testGroup_OneDevice(self):
with ops.Graph().as_default() as g:
with g.device("/task:0"):
a = tf.constant(0, name="a")
b = tf.constant(0, name="b")
tf.group(a.op, b.op, name="root")
gd = g.as_graph_def()
self.assertProtoEquals("""
node { name: "a" op: "Const" device: "/task:0" }
node { name: "b" op: "Const" device: "/task:0" }
node { name: "root" op: "NoOp" input: "^a" input: "^b" device: "/task:0" }
""", self._StripGraph(gd))
def testGroup_OneDevice(self):
with ops.Graph().as_default() as g:
with g.device("/task:0"):
a = tf.constant(0, name="a")
b = tf.constant(0, name="b")
tf.group(a.op, b.op, name="root")
gd = g.as_graph_def()
self.assertProtoEquals("""
node { name: "a" op: "Const" device: "/task:0" }
node { name: "b" op: "Const" device: "/task:0" }
node { name: "root" op: "NoOp" input: "^a" input: "^b" device: "/task:0" }
""", self._StripGraph(gd))
def testCondContext(self):
with self.test_session() as sess:
x = tf.constant(2)
y = tf.constant(5)
control_flow_ops.cond(tf.less(x, y),
lambda: tf.mul(x, 17),
lambda: tf.add(y, 23))
for op in sess.graph.get_operations():
c = op._get_control_flow_context()
if c:
compare.ProtoEq(
c.to_proto(),
control_flow_ops.CondContext.from_proto(c.to_proto()).to_proto())
def testGroup_NoDevices(self):
with ops.Graph().as_default() as g:
a = tf.constant(0, name="a")
b = tf.constant(0, name="b")
c = tf.constant(0, name="c")
tf.group(a.op, b.op, c.op, name="root")
gd = g.as_graph_def()
self.assertProtoEquals("""
node { name: "a" op: "Const"}
node { name: "b" op: "Const"}
node { name: "c" op: "Const"}
node { name: "root" op: "NoOp" input: "^a" input: "^b" input: "^c" }
""", self._StripGraph(gd))
def testGroup_NoDevices(self):
with ops.Graph().as_default() as g:
a = tf.constant(0, name="a")
b = tf.constant(0, name="b")
c = tf.constant(0, name="c")
tf.group(a.op, b.op, c.op, name="root")
gd = g.as_graph_def()
self.assertProtoEquals("""
node { name: "a" op: "Const"}
node { name: "b" op: "Const"}
node { name: "c" op: "Const"}
node { name: "root" op: "NoOp" input: "^a" input: "^b" input: "^c" }
""", self._StripGraph(gd))
def testCondContext(self):
with self.test_session() as sess:
x = tf.constant(2)
y = tf.constant(5)
control_flow_ops.cond(tf.less(x, y), lambda: tf.mul(x, 17),
lambda: tf.add(y, 23))
for op in sess.graph.get_operations():
c = op._get_control_flow_context()
if c:
compare.ProtoEq(
c.to_proto(),
control_flow_ops.CondContext.from_proto(
c.to_proto()).to_proto())
def testIndexedSlicesWithDynamicShapeGradientInWhileLoop(self):
for dtype in [dtypes.float32, dtypes.float64]:
with self.test_session() as sess:
inputs = tf.placeholder(dtype=dtype)
initial_outputs = tf.TensorArray(dtype=dtype, dynamic_size=True,
size=1)
initial_i = tf.constant(0, dtype=dtypes.int32)
def Cond(i, _):
return i < tf.size(inputs) # pylint: disable=cell-var-from-loop
def Body(i, outputs):
x = tf.gather(inputs, i) # pylint: disable=cell-var-from-loop
outputs = outputs.write(i, x)
return i + 1, outputs
_, outputs = tf.while_loop(Cond, Body, [initial_i, initial_outputs])
outputs = tf.reduce_sum(outputs.pack())
r = tf.gradients([outputs], [inputs])[0]
grad_wr_inputs = ops.convert_to_tensor(r)
o, grad = sess.run([outputs, grad_wr_inputs],
feed_dict={inputs: [1, 3, 2]})
self.assertEquals(o, 6)
self.assertAllEqual(grad, [1] * 3)
def testIndexedSlicesWithShapeGradientInWhileLoop(self):
with self.test_session() as sess:
num_steps = 9
inputs = tf.placeholder(dtype="float32", shape=[num_steps])
initial_outputs = tf.TensorArray(dtype="float32", size=num_steps)
initial_i = tf.constant(0, dtype="int32")
def Cond(i, _):
return i < num_steps
def Body(i, outputs):
x = tf.gather(inputs, i)
outputs = outputs.write(i, x)
return i + 1, outputs
_, outputs = tf.while_loop(Cond, Body, [initial_i, initial_outputs])
outputs = tf.reduce_sum(outputs.pack())
r = tf.gradients([outputs], [inputs])[0]
grad_wr_inputs = ops.convert_to_tensor(r)
o, grad = sess.run([outputs, grad_wr_inputs],
feed_dict={inputs: [4, 6, 0, 7, 0, 0, 1, 2, 0]})
self.assertEquals(o, 20)
self.assertAllEqual(grad, [1] * num_steps)
def _maximal_eigenvector_power_method(matrix,
epsilon=1e-6,
maximum_iterations=100):
"""Returns the maximal right-eigenvector of `matrix` using the power method.
Args:
matrix: 2D Tensor, the matrix of which we will find the maximal
right-eigenvector.
epsilon: nonnegative float, if two iterations of the power method differ (in
L2 norm) by no more than epsilon, we will terminate.
maximum_iterations: nonnegative int, if we perform this many iterations, we
will terminate.
Result:
The maximal right-eigenvector of `matrix`.
Raises:
ValueError: If the `matrix` tensor is not floating-point, or if the
`epsilon` or `maximum_iterations` parameters violate their bounds.
"""
if not matrix.dtype.is_floating:
raise ValueError("multipliers must have a floating-point dtype")
if epsilon <= 0.0:
raise ValueError("epsilon must be strictly positive")
if maximum_iterations <= 0:
raise ValueError("maximum_iterations must be strictly positive")
def while_loop_condition(iteration, eigenvector, old_eigenvector):
"""Returns false if the while loop should terminate."""
not_done = (iteration < maximum_iterations)
not_converged = (standard_ops.norm(eigenvector - old_eigenvector) > epsilon)
return standard_ops.logical_and(not_done, not_converged)
def while_loop_body(iteration, eigenvector, old_eigenvector):
"""Performs one iteration of the power method."""
del old_eigenvector # Needed by the condition, but not the body.
iteration += 1
# We need to use tf.matmul() and tf.expand_dims(), instead of
# tf.tensordot(), since the former will infer the shape of the result, while
# the latter will not (tf.while_loop() needs the shapes).
new_eigenvector = standard_ops.matmul(
matrix, standard_ops.expand_dims(eigenvector, 1))[:, 0]
new_eigenvector /= standard_ops.norm(new_eigenvector)
return (iteration, new_eigenvector, eigenvector)
iteration = standard_ops.constant(0)
eigenvector = standard_ops.ones_like(matrix[:, 0])
eigenvector /= standard_ops.norm(eigenvector)
# We actually want a do-while loop, so we explicitly call while_loop_body()
# once before tf.while_loop().
iteration, eigenvector, old_eigenvector = while_loop_body(
iteration, eigenvector, eigenvector)
iteration, eigenvector, old_eigenvector = control_flow_ops.while_loop(
while_loop_condition,
while_loop_body,
loop_vars=(iteration, eigenvector, old_eigenvector),
name="power_method")
return eigenvector
def testIndexedSlicesWithDynamicShapeGradientInWhileLoop(self):
for dtype in [dtypes.float32, dtypes.float64]:
with self.test_session() as sess:
inputs = tf.placeholder(dtype=dtype)
initial_outputs = tf.TensorArray(dtype=dtype,
dynamic_size=True,
size=1)
initial_i = tf.constant(0, dtype=dtypes.int32)
def Cond(i, _):
return i < tf.size(inputs) # pylint: disable=cell-var-from-loop
def Body(i, outputs):
x = tf.gather(inputs, i) # pylint: disable=cell-var-from-loop
outputs = outputs.write(i, x)
return i + 1, outputs
_, outputs = tf.while_loop(Cond, Body,
[initial_i, initial_outputs])
outputs = tf.reduce_sum(outputs.pack())
r = tf.gradients([outputs], [inputs])[0]
grad_wr_inputs = ops.convert_to_tensor(r)
o, grad = sess.run([outputs, grad_wr_inputs],
feed_dict={inputs: [1, 3, 2]})
self.assertEquals(o, 6)
self.assertAllEqual(grad, [1] * 3)
def _maximal_eigenvector_power_method(matrix,
epsilon=1e-6,
maximum_iterations=100):
"""Returns the maximal right-eigenvector of `matrix` using the power method.
Args:
matrix: 2D Tensor, the matrix of which we will find the maximal
right-eigenvector.
epsilon: nonnegative float, if two iterations of the power method differ (in
L2 norm) by no more than epsilon, we will terminate.
maximum_iterations: nonnegative int, if we perform this many iterations, we
will terminate.
Result: The maximal right-eigenvector of `matrix`.
Raises:
ValueError: If the `matrix` tensor is not floating-point, or if the
`epsilon` or `maximum_iterations` parameters violate their bounds.
"""
if not matrix.dtype.is_floating:
raise ValueError("multipliers must have a floating-point dtype")
if epsilon <= 0.0:
raise ValueError("epsilon must be strictly positive")
if maximum_iterations <= 0:
raise ValueError("maximum_iterations must be strictly positive")
def while_loop_condition(iteration, eigenvector, old_eigenvector):
"""Returns false if the while loop should terminate."""
not_done = (iteration < maximum_iterations)
not_converged = (standard_ops.norm(eigenvector - old_eigenvector) >
epsilon)
return standard_ops.logical_and(not_done, not_converged)
def while_loop_body(iteration, eigenvector, old_eigenvector):
"""Performs one iteration of the power method."""
del old_eigenvector # Needed by the condition, but not the body.
iteration += 1
# We need to use tf.matmul() and tf.expand_dims(), instead of
# tf.tensordot(), since the former will infer the shape of the result, while
# the latter will not (tf.while_loop() needs the shapes).
new_eigenvector = standard_ops.matmul(
matrix, standard_ops.expand_dims(eigenvector, 1))[:, 0]
new_eigenvector /= standard_ops.norm(new_eigenvector)
return (iteration, new_eigenvector, eigenvector)
iteration = standard_ops.constant(0)
eigenvector = standard_ops.ones_like(matrix[:, 0])
eigenvector /= standard_ops.norm(eigenvector)
# We actually want a do-while loop, so we explicitly call while_loop_body()
# once before tf.while_loop().
iteration, eigenvector, old_eigenvector = while_loop_body(
iteration, eigenvector, eigenvector)
iteration, eigenvector, old_eigenvector = control_flow_ops.while_loop(
while_loop_condition,
while_loop_body,
loop_vars=(iteration, eigenvector, old_eigenvector),
name="power_method")
return eigenvector
def _initial_state(self, num_constraints):
# For a MultiplicativeSwapRegretOptimizer, the internal state is a tensor of
# shape (m+1,m+1), where m is the number of constraints, representing the
# element-wise logarithm of a left-stochastic matrix.
dimension = num_constraints + 1
# Initialize by putting as much weight as possible on the objective, and as
# little as possible on the constraints.
log_initial_one = math.log(1.0 - (self._initial_multiplier_radius *
(dimension - 1) / (dimension)))
log_initial_zero = math.log(self._initial_multiplier_radius / dimension)
return standard_ops.concat(
(standard_ops.constant(
log_initial_one, dtype=dtypes.float32, shape=(1, dimension)),
standard_ops.constant(
log_initial_zero,
dtype=dtypes.float32,
shape=(dimension - 1, dimension))),
axis=0)
def testIndexedSlicesGradient(self):
with ops.Graph().as_default():
embedding_matrix = tf.get_variable(
"embedding_matrix", [5, 5],
initializer=tf.random_normal_initializer())
def Cond(it, _):
return it < 5
def Body(it, cost):
embedding = embedding_ops.embedding_lookup(embedding_matrix + 0.0, [0])
cost += tf.reduce_sum(embedding)
return it + 1, cost
_, cost = control_flow_ops.While(
Cond, Body, [tf.constant(0), tf.constant(0.0)])
optimizer = momentum.MomentumOptimizer(0.1, 0.9)
train_op = optimizer.minimize(cost)
with self.test_session() as sess:
sess.run(tf.initialize_all_variables())
for _ in range(10):
sess.run([train_op])
def test_maximum_eigenvector_power_method(self):
"""Tests power method routine on some known left-stochastic matrices."""
matrix1 = np.matrix([[0.6, 0.1, 0.1], [0.0, 0.6, 0.9], [0.4, 0.3, 0.0]])
matrix2 = np.matrix([[0.4, 0.4, 0.2], [0.2, 0.1, 0.5], [0.4, 0.5, 0.3]])
with self.test_session() as session:
eigenvector1 = session.run(
swap_regret_optimizer._maximal_eigenvector_power_method(
standard_ops.constant(matrix1)))
eigenvector2 = session.run(
swap_regret_optimizer._maximal_eigenvector_power_method(
standard_ops.constant(matrix2)))
# Check that eigenvector1 and eigenvector2 are eigenvectors of matrix1 and
# matrix2 (respectively) with associated eigenvalue 1.
matrix_eigenvector1 = np.tensordot(matrix1, eigenvector1, axes=1)
matrix_eigenvector2 = np.tensordot(matrix2, eigenvector2, axes=1)
self.assertAllClose(eigenvector1, matrix_eigenvector1, rtol=0, atol=1e-6)
self.assertAllClose(eigenvector2, matrix_eigenvector2, rtol=0, atol=1e-6)
def testWhileContext(self):
with self.test_session() as sess:
i = tf.constant(0)
c = lambda i: tf.less(i, 10)
b = lambda i: tf.add(i, 1)
tf.while_loop(c, b, [i])
for op in sess.graph.get_operations():
c = op._get_control_flow_context()
if c:
compare.ProtoEq(
c.to_proto(),
control_flow_ops.WhileContext.from_proto(c.to_proto()).to_proto())
def testWhileContext(self):
with self.test_session() as sess:
i = tf.constant(0)
c = lambda i: tf.less(i, 10)
b = lambda i: tf.add(i, 1)
tf.while_loop(c, b, [i])
for op in sess.graph.get_operations():
c = op._get_control_flow_context()
if c:
compare.ProtoEq(
c.to_proto(),
control_flow_ops.WhileContext.from_proto(
c.to_proto()).to_proto())
def __init__(self, constraints):
"""Constructs a new `ConstantMinimizationProblem'.
Args:
constraints: 1d numpy array, the constant constraint violations.
Returns:
A new `ConstantMinimizationProblem'.
"""
# We make an fake 1-parameter linear objective so that we don't get a "no
# variables to optimize" error.
self._objective = standard_ops.Variable(0.0, dtype=dtypes.float32)
self._constraints = standard_ops.constant(constraints, dtype=dtypes.float32)
def test_project_stochastic_matrix_wrt_euclidean_norm(self):
"""Tests Euclidean projection routine on some known values."""
matrix = standard_ops.constant([[-0.1, -0.1, 0.4], [-0.8, 0.4, 1.2],
[-0.3, 0.1, 0.2]])
expected_projected_matrix = np.array([[0.6, 0.1, 0.1], [0.0, 0.6, 0.9],
[0.4, 0.3, 0.0]])
with self.test_session() as session:
projected_matrix = session.run(
swap_regret_optimizer._project_stochastic_matrix_wrt_euclidean_norm(
matrix))
self.assertAllClose(
expected_projected_matrix, projected_matrix, rtol=0, atol=1e-6)
def test_project_stochastic_matrix_wrt_euclidean_norm(self):
"""Tests Euclidean projection routine on some known values."""
matrix = standard_ops.constant([[-0.1, -0.1, 0.4], [-0.8, 0.4, 1.2],
[-0.3, 0.1, 0.2]])
expected_projected_matrix = np.array([[0.6, 0.1, 0.1], [0.0, 0.6, 0.9],
[0.4, 0.3, 0.0]])
with self.cached_session() as session:
projected_matrix = session.run(
swap_regret_optimizer._project_stochastic_matrix_wrt_euclidean_norm(
matrix))
self.assertAllClose(
expected_projected_matrix, projected_matrix, rtol=0, atol=1e-6)
def __init__(self, constraints):
"""Constructs a new `ConstantMinimizationProblem'.
Args:
constraints: 1d numpy array, the constant constraint violations.
Returns:
A new `ConstantMinimizationProblem'.
"""
# We make an fake 1-parameter linear objective so that we don't get a "no
# variables to optimize" error.
self._objective = standard_ops.Variable(0.0, dtype=dtypes.float32)
self._constraints = standard_ops.constant(constraints,
dtype=dtypes.float32)
def testGroup_MultiDevice(self):
with ops.Graph().as_default() as g:
with g.device("/task:0"):
a = tf.constant(0, name="a")
b = tf.constant(0, name="b")
with g.device("/task:1"):
c = tf.constant(0, name="c")
d = tf.constant(0, name="d")
with g.device("/task:2"):
tf.group(a.op, b.op, c.op, d.op, name="root")
gd = g.as_graph_def()
self.assertProtoEquals("""
node { name: "a" op: "Const" device: "/task:0"}
node { name: "b" op: "Const" device: "/task:0"}
node { name: "c" op: "Const" device: "/task:1"}
node { name: "d" op: "Const" device: "/task:1"}
node { name: "root/NoOp" op: "NoOp" input: "^a" input: "^b"
device: "/task:0" }
node { name: "root/NoOp_1" op: "NoOp" input: "^c" input: "^d"
device: "/task:1" }
node { name: "root" op: "NoOp" input: "^root/NoOp" input: "^root/NoOp_1"
device: "/task:2" }
""", self._StripGraph(gd))
def test_project_multipliers_wrt_euclidean_norm(self):
"""Tests Euclidean projection routine on some known values."""
multipliers1 = standard_ops.constant([-0.1, -0.6, -0.3])
expected_projected_multipliers1 = np.array([0.0, 0.0, 0.0])
multipliers2 = standard_ops.constant([-0.1, 0.6, 0.3])
expected_projected_multipliers2 = np.array([0.0, 0.6, 0.3])
multipliers3 = standard_ops.constant([0.4, 0.7, -0.2, 0.5, 0.1])
expected_projected_multipliers3 = np.array([0.2, 0.5, 0.0, 0.3, 0.0])
with self.test_session() as session:
projected_multipliers1 = session.run(
external_regret_optimizer._project_multipliers_wrt_euclidean_norm(
multipliers1, 1.0))
projected_multipliers2 = session.run(
external_regret_optimizer._project_multipliers_wrt_euclidean_norm(
multipliers2, 1.0))
projected_multipliers3 = session.run(
external_regret_optimizer._project_multipliers_wrt_euclidean_norm(
multipliers3, 1.0))
self.assertAllClose(
expected_projected_multipliers1,
projected_multipliers1,
rtol=0,
atol=1e-6)
self.assertAllClose(
expected_projected_multipliers2,
projected_multipliers2,
rtol=0,
atol=1e-6)
self.assertAllClose(
expected_projected_multipliers3,
projected_multipliers3,
rtol=0,
atol=1e-6)
def test_project_log_stochastic_matrix_wrt_kl_divergence(self):
"""Tests KL-divergence projection routine on some known values."""
matrix = standard_ops.constant([[0.2, 0.8, 0.6], [0.1, 0.2, 1.5],
[0.2, 1.0, 0.9]])
expected_projected_matrix = np.array([[0.4, 0.4, 0.2], [0.2, 0.1, 0.5],
[0.4, 0.5, 0.3]])
with self.cached_session() as session:
projected_matrix = session.run(
standard_ops.exp(
swap_regret_optimizer.
_project_log_stochastic_matrix_wrt_kl_divergence(
standard_ops.log(matrix))))
self.assertAllClose(
expected_projected_matrix, projected_matrix, rtol=0, atol=1e-6)
def test_project_log_stochastic_matrix_wrt_kl_divergence(self):
"""Tests KL-divergence projection routine on some known values."""
matrix = standard_ops.constant([[0.2, 0.8, 0.6], [0.1, 0.2, 1.5],
[0.2, 1.0, 0.9]])
expected_projected_matrix = np.array([[0.4, 0.4, 0.2], [0.2, 0.1, 0.5],
[0.4, 0.5, 0.3]])
with self.test_session() as session:
projected_matrix = session.run(
standard_ops.exp(
swap_regret_optimizer.
_project_log_stochastic_matrix_wrt_kl_divergence(
standard_ops.log(matrix))))
self.assertAllClose(
expected_projected_matrix, projected_matrix, rtol=0, atol=1e-6)
def _project_multipliers_wrt_euclidean_norm(multipliers, radius):
"""Projects its argument onto the feasible region.
The feasible region is the set of all vectors with nonnegative elements that
sum to at most `radius`.
Args:
multipliers: 1d tensor, the Lagrange multipliers to project.
radius: float, the radius of the feasible region.
Returns:
The 1d tensor that results from projecting `multipliers` onto the feasible
region w.r.t. the Euclidean norm.
Raises:
ValueError: if the `multipliers` tensor is not floating-point, does not have
a fully-known shape, or is not one-dimensional.
"""
if not multipliers.dtype.is_floating:
raise ValueError("multipliers must have a floating-point dtype")
multipliers_shape = multipliers.get_shape()
if multipliers_shape.ndims is None:
raise ValueError("multipliers must have known shape")
if multipliers_shape.ndims != 1:
raise ValueError(
"multipliers must be one dimensional (instead is %d-dimensional)" %
multipliers_shape.ndims)
dimension = multipliers_shape[0].value
if dimension is None:
raise ValueError("multipliers must have fully-known shape")
def while_loop_condition(iteration, multipliers, inactive, old_inactive):
"""Returns false if the while loop should terminate."""
del multipliers # Needed by the body, but not the condition.
not_done = (iteration < dimension)
not_converged = standard_ops.reduce_any(
standard_ops.not_equal(inactive, old_inactive))
return standard_ops.logical_and(not_done, not_converged)
def while_loop_body(iteration, multipliers, inactive, old_inactive):
"""Performs one iteration of the projection."""
del old_inactive # Needed by the condition, but not the body.
iteration += 1
scale = standard_ops.minimum(
0.0,
(radius - standard_ops.reduce_sum(multipliers)) / standard_ops.maximum(
1.0, standard_ops.reduce_sum(inactive)))
multipliers += scale * inactive
new_inactive = standard_ops.cast(multipliers > 0, multipliers.dtype)
multipliers *= new_inactive
return (iteration, multipliers, new_inactive, inactive)
iteration = standard_ops.constant(0)
inactive = standard_ops.ones_like(multipliers, dtype=multipliers.dtype)
# We actually want a do-while loop, so we explicitly call while_loop_body()
# once before tf.while_loop().
iteration, multipliers, inactive, old_inactive = while_loop_body(
iteration, multipliers, inactive, inactive)
iteration, multipliers, inactive, old_inactive = control_flow_ops.while_loop(
while_loop_condition,
while_loop_body,
loop_vars=(iteration, multipliers, inactive, old_inactive),
name="euclidean_projection")
return multipliers
def _project_multipliers_wrt_euclidean_norm(multipliers, radius):
"""Projects its argument onto the feasible region.
The feasible region is the set of all vectors with nonnegative elements that
sum to at most `radius`.
Args:
multipliers: 1d tensor, the Lagrange multipliers to project.
radius: float, the radius of the feasible region.
Returns:
The 1d tensor that results from projecting `multipliers` onto the feasible
region w.r.t. the Euclidean norm.
Raises:
ValueError: if the `multipliers` tensor is not floating-point, does not have
a fully-known shape, or is not one-dimensional.
"""
if not multipliers.dtype.is_floating:
raise ValueError("multipliers must have a floating-point dtype")
multipliers_shape = multipliers.get_shape()
if multipliers_shape.ndims is None:
raise ValueError("multipliers must have known shape")
if multipliers_shape.ndims != 1:
raise ValueError(
"multipliers must be one dimensional (instead is %d-dimensional)" %
multipliers_shape.ndims)
dimension = multipliers_shape[0].value
if dimension is None:
raise ValueError("multipliers must have fully-known shape")
def while_loop_condition(iteration, multipliers, inactive, old_inactive):
"""Returns false if the while loop should terminate."""
del multipliers # Needed by the body, but not the condition.
not_done = (iteration < dimension)
not_converged = standard_ops.reduce_any(
standard_ops.not_equal(inactive, old_inactive))
return standard_ops.logical_and(not_done, not_converged)
def while_loop_body(iteration, multipliers, inactive, old_inactive):
"""Performs one iteration of the projection."""
del old_inactive # Needed by the condition, but not the body.
iteration += 1
scale = standard_ops.minimum(
0.0, (radius - standard_ops.reduce_sum(multipliers)) /
standard_ops.maximum(1.0, standard_ops.reduce_sum(inactive)))
multipliers = multipliers + (scale * inactive)
new_inactive = standard_ops.cast(multipliers > 0, multipliers.dtype)
multipliers = multipliers * new_inactive
return (iteration, multipliers, new_inactive, inactive)
iteration = standard_ops.constant(0)
inactive = standard_ops.ones_like(multipliers, dtype=multipliers.dtype)
# We actually want a do-while loop, so we explicitly call while_loop_body()
# once before tf.while_loop().
iteration, multipliers, inactive, old_inactive = while_loop_body(
iteration, multipliers, inactive, inactive)
iteration, multipliers, inactive, old_inactive = control_flow_ops.while_loop(
while_loop_condition,
while_loop_body,
loop_vars=(iteration, multipliers, inactive, old_inactive),
name="euclidean_projection")
return multipliers
def _project_stochastic_matrix_wrt_euclidean_norm(matrix):
"""Projects its argument onto the set of left-stochastic matrices.
This algorithm is O(n^3) at worst, where `matrix` is n*n. It can be done in
O(n^2 * log(n)) time by sorting each column (and maybe better with a different
algorithm), but the algorithm implemented here is easier to implement in
TensorFlow.
Args:
matrix: 2d square tensor, the matrix to project.
Returns:
The 2d square tensor that results from projecting `matrix` onto the set of
left-stochastic matrices w.r.t. the Euclidean norm applied column-wise
(i.e. the Frobenius norm).
Raises:
ValueError: if the `matrix` tensor is not floating-point, does not have a
fully-known shape, or is not two-dimensional and square.
"""
if not matrix.dtype.is_floating:
raise ValueError("multipliers must have a floating-point dtype")
matrix_shape = matrix.get_shape()
if matrix_shape.ndims is None:
raise ValueError("matrix must have known shape")
if matrix_shape.ndims != 2:
raise ValueError(
"matrix must be two dimensional (instead is %d-dimensional)" %
matrix_shape.ndims)
if matrix_shape[0] != matrix_shape[1]:
raise ValueError("matrix must be square (instead has shape (%d,%d))" %
(matrix_shape[0], matrix_shape[1]))
dimension = matrix_shape[0].value
if dimension is None:
raise ValueError("matrix must have fully-known shape")
def while_loop_condition(iteration, matrix, inactive, old_inactive):
"""Returns false if the while loop should terminate."""
del matrix # Needed by the body, but not the condition.
not_done = (iteration < dimension)
not_converged = standard_ops.reduce_any(
standard_ops.not_equal(inactive, old_inactive))
return standard_ops.logical_and(not_done, not_converged)
def while_loop_body(iteration, matrix, inactive, old_inactive):
"""Performs one iteration of the projection."""
del old_inactive # Needed by the condition, but not the body.
iteration += 1
scale = (1.0 - standard_ops.reduce_sum(
matrix, axis=0, keepdims=True)) / standard_ops.maximum(
1.0, standard_ops.reduce_sum(inactive, axis=0, keepdims=True))
matrix += scale * inactive
new_inactive = standard_ops.cast(matrix > 0, matrix.dtype)
matrix *= new_inactive
return (iteration, matrix, new_inactive, inactive)
iteration = standard_ops.constant(0)
inactive = standard_ops.ones_like(matrix, dtype=matrix.dtype)
# We actually want a do-while loop, so we explicitly call while_loop_body()
# once before tf.while_loop().
iteration, matrix, inactive, old_inactive = while_loop_body(
iteration, matrix, inactive, inactive)
iteration, matrix, inactive, old_inactive = control_flow_ops.while_loop(
while_loop_condition,
while_loop_body,
loop_vars=(iteration, matrix, inactive, old_inactive),
name="euclidean_projection")
return matrix