Applies the L-BFGS algorithm to minimize a differentiable function.
value_and_gradients_function, initial_position, previous_optimizer_results=None,
num_correction_pairs=10, tolerance=1e-08, x_tolerance=0, f_relative_tolerance=0,
initial_inverse_hessian_estimate=None, max_iterations=50, parallel_iterations=1,
stopping_condition=None, max_line_search_iterations=50, name=None
Performs unconstrained minimization of a differentiable function using the
L-BFGS scheme. See [Nocedal and Wright(2006)] for details of the algorithm.
The following example demonstrates the L-BFGS optimizer attempting to find the
minimum for a simple high-dimensional quadratic objective function.
# A high-dimensional quadratic bowl.
ndims = 60
minimum = np.ones([ndims], dtype='float64')
scales = np.arange(ndims, dtype='float64') + 1.0
# The objective function and the gradient.
lambda x: tf.reduce_sum(
scales * tf.math.squared_difference(x, minimum), axis=-1),
start = np.arange(ndims, 0, -1, dtype='float64')
optim_results = tfp.optimizer.lbfgs_minimize(
# Check that the search converged
# Check that the argmin is close to the actual value.
 Jorge Nocedal, Stephen Wright. Numerical Optimization. Springer Series
in Operations Research. pp 176-180. 2006
A Python callable that accepts a point as a
Tensor and returns a tuple of
Tensors of real dtype containing
the value of the function and its gradient at that point. The function
to be minimized. The input is of shape
[..., n], where
n is the size
of the domain of input points, and all others are batching dimensions.
The first component of the return value is a real
Tensor of matching
[...]. The second component (the gradient) is also of shape
[..., n] like the input value to the function.
Tensor of shape
[..., n]. The starting point, or
points when using batching dimensions, of the search procedure. At these
points the function value and the gradient norm should be finite.
Exactly one of
previous_optimizer_results can be
LBfgsOptimizerResults namedtuple to
intialize the optimizer state from, instead of an
This can be passed in from a previous return value to resume optimization
with a different
stopping_condition. Exactly one of
previous_optimizer_results can be non-None.
Positive integer. Specifies the maximum number of
(position_delta, gradient_delta) correction pairs to keep as implicit
approximation of the Hessian matrix.
Tensor of real dtype. Specifies the gradient tolerance
for the procedure. If the supremum norm of the gradient vector is below
this number, the algorithm is stopped.
Tensor of real dtype. If the absolute change in the
position between one iteration and the next is smaller than this number,
the algorithm is stopped.
Tensor of real dtype. If the relative change
in the objective value between one iteration and the next is smaller
than this value, the algorithm is stopped.
None. Option currently not supported.
Scalar positive int32
Tensor. The maximum number of
iterations for L-BFGS updates.
Positive integer. The number of iterations allowed to
run in parallel.
(Optional) A Python function that takes as input two
Boolean tensors of shape
[...], and returns a Boolean scalar tensor.
The input tensors are
failed, indicating the current
status of each respective batch member; the return value states whether
the algorithm should stop. The default is tfp.optimizer.converged_all
which only stops when all batch members have either converged or failed.
An alternative is tfp.optimizer.converged_any which stops as soon as one
batch member has converged, or when all have failed.
Python int. The maximum number of iterations
hager_zhang line search algorithm.
(Optional) Python str. The name prefixed to the ops created by this
function. If not supplied, the default name 'minimize' is used.
A namedtuple containing the following items:
converged: Scalar boolean tensor indicating whether the minimum was
found within tolerance.
failed: Scalar boolean tensor indicating whether a line search
step failed to find a suitable step size satisfying Wolfe
conditions. In the absence of any constraints on the
number of objective evaluations permitted, this value will
be the complement of
converged. However, if there is
a constraint and the search stopped due to available
evaluations being exhausted, both
will be simultaneously False.
num_objective_evaluations: The total number of objective
position: A tensor containing the last argument value found
during the search. If the search converged, then
this value is the argmin of the objective function.
objective_value: A tensor containing the value of the objective
function at the
position. If the search converged, then this is
the (local) minimum of the objective function.
objective_gradient: A tensor containing the gradient of the objective
function at the
position. If the search converged the
max-norm of this tensor should be below the tolerance.
position_deltas: A tensor encoding information about the latest
position during the algorithm execution.
gradient_deltas: A tensor encoding information about the latest
objective_gradient during the algorithm execution.