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 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 _project_log_stochastic_matrix_wrt_kl_divergence(log_matrix):
"""Projects its argument onto the set of log-left-stochastic matrices.
Args:
log_matrix: 2d square tensor, the element-wise logarithm of the matrix to
project.
Returns:
The 2d square tensor that results from projecting exp(`matrix`) onto the set
of left-stochastic matrices w.r.t. the KL-divergence applied column-wise.
"""
# For numerical reasons, make sure that the largest matrix element is zero
# before exponentiating.
log_matrix -= standard_ops.reduce_max(log_matrix, axis=0, keepdims=True)
log_matrix -= standard_ops.log(
standard_ops.reduce_sum(
standard_ops.exp(log_matrix), axis=0, keepdims=True))
return log_matrix
def _project_log_stochastic_matrix_wrt_kl_divergence(log_matrix):
"""Projects its argument onto the set of log-left-stochastic matrices.
Args:
log_matrix: 2d square tensor, the element-wise logarithm of the matrix to
project.
Returns:
The 2d square tensor that results from projecting exp(`matrix`) onto the set
of left-stochastic matrices w.r.t. the KL-divergence applied column-wise.
"""
# For numerical reasons, make sure that the largest matrix element is zero
# before exponentiating.
log_matrix -= standard_ops.reduce_max(log_matrix, axis=0, keep_dims=True)
log_matrix -= standard_ops.log(
standard_ops.reduce_sum(
standard_ops.exp(log_matrix), axis=0, keep_dims=True))
return log_matrix
def _projection_op(self, state, name=None):
with ops.colocate_with(state):
# Gets the dimension of the state (num_constraints + 1)--all of these
# assertions are of things that should be impossible, since the state
# passed into this method will have the same shape as that returned by
# _initial_state().
state_shape = state.get_shape()
assert state_shape is not None
assert state_shape.ndims == 2
assert state_shape[0] == state_shape[1]
dimension = state_shape.dims[0].value
assert dimension is not None
minimum_log_multiplier = standard_ops.log(
self._minimum_multiplier_radius / standard_ops.to_float(dimension))
return state_ops.assign(
state,
standard_ops.maximum(
_project_log_stochastic_matrix_wrt_kl_divergence(state),
minimum_log_multiplier),
name=name)
def _projection_op(self, state, name=None):
with ops.colocate_with(state):
# Gets the dimension of the state (num_constraints + 1)--all of these
# assertions are of things that should be impossible, since the state
# passed into this method will have the same shape as that returned by
# _initial_state().
state_shape = state.get_shape()
assert state_shape is not None
assert state_shape.ndims == 2
assert state_shape[0] == state_shape[1]
dimension = state_shape[0].value
assert dimension is not None
minimum_log_multiplier = standard_ops.log(
self._minimum_multiplier_radius / standard_ops.to_float(dimension))
return state_ops.assign(
state,
standard_ops.maximum(
_project_log_stochastic_matrix_wrt_kl_divergence(state),
minimum_log_multiplier),
name=name)