wehub-resource-sync
827 lines
30 KiB
Python
827 lines
30 KiB
Python
# Copyright (c) 2022 PaddlePaddle 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.
|
|
|
|
from __future__ import annotations
|
|
|
|
import os
|
|
import warnings
|
|
from collections import defaultdict
|
|
from functools import reduce
|
|
from typing import TYPE_CHECKING, NoReturn, TypedDict
|
|
|
|
from typing_extensions import NotRequired
|
|
|
|
import paddle
|
|
|
|
from ..base import framework
|
|
from .optimizer import Optimizer
|
|
|
|
if TYPE_CHECKING:
|
|
from collections.abc import Sequence
|
|
|
|
from paddle import Tensor
|
|
from paddle.nn.clip import GradientClipBase
|
|
from paddle.regularizer import WeightDecayRegularizer
|
|
|
|
from .optimizer import _ParameterConfig
|
|
|
|
__all__ = []
|
|
|
|
|
|
class _LbfgsState(TypedDict):
|
|
func_evals: int
|
|
n_iter: int
|
|
d: Tensor
|
|
alpha: Tensor
|
|
old_yk: list[Tensor]
|
|
old_sk: list[Tensor]
|
|
ro: list[Tensor]
|
|
H_diag: Tensor
|
|
prev_flat_grad: Tensor
|
|
prev_loss: float
|
|
al: NotRequired[list[Tensor]]
|
|
|
|
|
|
class _LbfgsStateDict(TypedDict):
|
|
state: _LbfgsState
|
|
|
|
|
|
def check_tf32_override():
|
|
"""Check and warn about TF32 acceleration status"""
|
|
if (
|
|
paddle.device.is_compiled_with_cuda()
|
|
and os.getenv("NVIDIA_TF32_OVERRIDE") != "0"
|
|
): # None or "1"
|
|
warnings.warn(
|
|
"Warning! TF32 Tensor Cores are enabled by default on some NVIDIA GPUs for faster computation, "
|
|
"but may compromise numerical precision in specific cases, particularly with the L-BFGS optimizer."
|
|
"To disable it, set: NVIDIA_TF32_OVERRIDE=0"
|
|
)
|
|
|
|
|
|
def dot(x, y):
|
|
r"""
|
|
NOTE: This is a temporary workaround for unstable result computed by `paddle.dot`,
|
|
which will be reverted when the problem is fixed."
|
|
"""
|
|
return (x * y).sum(axis=-1)
|
|
|
|
|
|
def _cubic_interpolate(x1, f1, g1, x2, f2, g2, bounds=None):
|
|
r"""Cubic interpolation between (x1, f1, g1) and (x2, f2, g2).
|
|
Use two points and their gradient to determine a cubic function and get the minimum point
|
|
between them in the cubic curve.
|
|
|
|
Reference:
|
|
Jorge Nocedal, Stephen J. Wright, Numerical Optimization, Second Edition, 2006.
|
|
pp59: formula 3.59
|
|
|
|
Args:
|
|
x1, f1, g1: point1's position, value and gradient.
|
|
x2, f2, g2: point2's position, value and gradient.
|
|
bounds: bounds of interpolation area
|
|
|
|
Returns:
|
|
min_pos: the minimum point between the specified points in the cubic curve.
|
|
"""
|
|
# Compute bounds of interpolation area
|
|
if bounds is not None:
|
|
xmin_bound, xmax_bound = bounds
|
|
else:
|
|
xmin_bound, xmax_bound = (x1, x2) if x1 <= x2 else (x2, x1)
|
|
|
|
d1 = g1 + g2 - 3 * (f1 - f2) / (x1 - x2)
|
|
d2_square = d1**2 - g1 * g2
|
|
if d2_square >= 0:
|
|
d2 = d2_square.sqrt()
|
|
if x1 <= x2:
|
|
min_pos = x2 - (x2 - x1) * ((g2 + d2 - d1) / (g2 - g1 + 2 * d2))
|
|
else:
|
|
min_pos = x1 - (x1 - x2) * ((g1 + d2 - d1) / (g1 - g2 + 2 * d2))
|
|
return min(max(min_pos, xmin_bound), xmax_bound)
|
|
else:
|
|
return (xmin_bound + xmax_bound) / 2.0
|
|
|
|
|
|
def _strong_wolfe(
|
|
obj_func,
|
|
xk,
|
|
alpha,
|
|
d,
|
|
loss,
|
|
grad,
|
|
gtd,
|
|
c1=1e-4,
|
|
c2=0.9,
|
|
tolerance_change=1e-9,
|
|
max_ls=25,
|
|
):
|
|
r"""Implements of line search algorithm that satisfies the strong Wolfe conditions using double zoom.
|
|
|
|
Reference:
|
|
Jorge Nocedal, Stephen J. Wright, Numerical Optimization, Second Edition, 2006.
|
|
pp60: Algorithm 3.5 (Line Search Algorithm).
|
|
|
|
Args:
|
|
obj_func: the objective function to minimize. ```` accepts a multivariate input and returns a scalar.
|
|
xk (Tensor): the starting point of the iterates.
|
|
alpha (Scalar): the initial step size.
|
|
d (Tensor): search direction.
|
|
loss (scalar): the initial loss
|
|
grad (Tensor): the initial grad
|
|
c1 (Scalar): parameter for sufficient decrease condition.
|
|
c2 (Scalar): parameter for curvature condition.
|
|
tolerance_change (Scalar): terminates if the change of function value/position/parameter between
|
|
two iterations is smaller than this value.
|
|
max_ls(int): max iteration of line search.
|
|
alpha_max (float): max step length.
|
|
|
|
Returns:
|
|
loss_new (Scaler): loss of obj_func at final alpha.
|
|
grad_new, (Tensor): derivative of obj_func at final alpha.
|
|
alpha(Tensor): optimal step length, or 0. if the line search algorithm did not converge.
|
|
ls_func_evals (Scaler): number of objective function called in line search process.
|
|
|
|
Following summarizes the essentials of the strong Wolfe line search algorithm.
|
|
Some notations used in the description:
|
|
|
|
- `func` denotes the objective function.
|
|
- `obi_func` is a function of step size alpha, restricting `obj_func` on a line.
|
|
|
|
obi_func = func(xk + alpha * d),
|
|
where xk is the position of k'th iterate, d is the line search direction(decent direction),
|
|
and a is the step size.
|
|
- alpha : substitute of alpha
|
|
- a1 is alpha of last iteration, which is alpha_(i-1).
|
|
- a2 is alpha of current iteration, which is alpha_i.
|
|
- a_lo is alpha in left position when calls zoom, which is alpha_low.
|
|
- a_hi is alpha in right position when calls zoom, which is alpha_high.
|
|
|
|
Line Search Algorithm:
|
|
repeat
|
|
Compute obi_func(a2) and derphi(a2).
|
|
1. If obi_func(a2) > obi_func(0) + c_1 * a2 * obi_func'(0) or [obi_func(a2) >= obi_func(a1) and i > 1],
|
|
alpha= zoom(a1, a2) and stop;
|
|
|
|
2. If |obi_func'(a2)| <= -c_2 * obi_func'(0),
|
|
alpha= a2 and stop;
|
|
|
|
3. If obi_func'(a2) >= 0,
|
|
alpha= zoom(a2, a1) and stop;
|
|
|
|
a1 = a2
|
|
a2 = min(2 * a2, a2)
|
|
i = i + 1
|
|
end(repeat)
|
|
|
|
zoom(a_lo, a_hi) Algorithm:
|
|
repeat
|
|
aj = cubic_interpolation(a_lo, a_hi)
|
|
Compute obi_func(aj) and derphi(aj).
|
|
1. If obi_func(aj) > obi_func(0) + c_1 * aj * obi_func'(0) or obi_func(aj) >= obi_func(a_lo),
|
|
then a_hi <- aj;
|
|
2.
|
|
2.1. If |obi_func'(aj)| <= -c_2 * obi_func'(0), then alpha= a2 and stop;
|
|
|
|
2.2. If obi_func'(aj) * (a2 - a1) >= 0, then a_hi = a_lo
|
|
|
|
a_lo = aj;
|
|
end(repeat)
|
|
|
|
reference: https://github.com/pytorch/pytorch
|
|
"""
|
|
|
|
d_norm = d.abs().max()
|
|
grad = grad.clone()
|
|
# evaluate objective and gradient using initial step
|
|
loss_new, grad_new = obj_func(xk, alpha, d)
|
|
ls_func_evals = 1
|
|
gtd_new = dot(grad_new, d)
|
|
|
|
# bracket an interval containing a point satisfying the Wolfe criteria
|
|
t_prev, f_prev, g_prev, gtd_prev = (0, loss, grad, gtd)
|
|
done = False
|
|
ls_iter = 0
|
|
while ls_iter < max_ls:
|
|
# check conditions
|
|
if loss_new > (loss + c1 * alpha * gtd) or (
|
|
ls_iter > 1 and loss_new >= f_prev
|
|
):
|
|
bracket = [t_prev, alpha]
|
|
bracket_f = [f_prev, loss_new]
|
|
bracket_g = [g_prev, grad_new.clone()]
|
|
bracket_gtd = [gtd_prev, gtd_new]
|
|
break
|
|
|
|
if abs(gtd_new) <= -c2 * gtd:
|
|
bracket = [alpha]
|
|
bracket_f = [loss_new]
|
|
bracket_g = [grad_new]
|
|
done = True
|
|
break
|
|
|
|
if gtd_new >= 0:
|
|
bracket = [t_prev, alpha]
|
|
bracket_f = [f_prev, loss_new]
|
|
bracket_g = [g_prev, grad_new.clone()]
|
|
bracket_gtd = [gtd_prev, gtd_new]
|
|
break
|
|
|
|
# interpolate
|
|
min_step = alpha + 0.01 * (alpha - t_prev)
|
|
max_step = alpha * 10
|
|
tmp = alpha
|
|
alpha = _cubic_interpolate(
|
|
t_prev,
|
|
f_prev,
|
|
gtd_prev,
|
|
alpha,
|
|
loss_new,
|
|
gtd_new,
|
|
bounds=(min_step, max_step),
|
|
)
|
|
|
|
# next step
|
|
t_prev = tmp
|
|
f_prev = loss_new
|
|
g_prev = grad_new.clone()
|
|
gtd_prev = gtd_new
|
|
|
|
loss_new, grad_new = obj_func(xk, alpha, d)
|
|
ls_func_evals += 1
|
|
gtd_new = dot(grad_new, d)
|
|
ls_iter += 1
|
|
|
|
# reached max number of iterations?
|
|
if ls_iter == max_ls:
|
|
bracket = [0, alpha]
|
|
bracket_f = [loss, loss_new]
|
|
bracket_g = [grad, grad_new]
|
|
|
|
# zoom phase: we now have a point satisfying the criteria, or
|
|
# a bracket around it. We refine the bracket until we find the
|
|
# exact point satisfying the criteria
|
|
insuf_progress = False
|
|
# find high and low points in bracket
|
|
low_pos, high_pos = (0, 1) if bracket_f[0] <= bracket_f[-1] else (1, 0)
|
|
while not done and ls_iter < max_ls:
|
|
# line-search bracket is so small
|
|
if abs(bracket[1] - bracket[0]) * d_norm < tolerance_change:
|
|
break
|
|
|
|
# compute new trial value
|
|
alpha = _cubic_interpolate(
|
|
bracket[0],
|
|
bracket_f[0],
|
|
bracket_gtd[0],
|
|
bracket[1],
|
|
bracket_f[1],
|
|
bracket_gtd[1],
|
|
)
|
|
|
|
# test that we are making sufficient progress:
|
|
# in case `alpha` is so close to boundary, we mark that we are making
|
|
# insufficient progress, and if
|
|
# + we have made insufficient progress in the last step, or
|
|
# + `alpha` is at one of the boundary,
|
|
# we will move `alpha` to a position which is `0.1 * len(bracket)`
|
|
# away from the nearest boundary point.
|
|
|
|
eps = 0.1 * (max(bracket) - min(bracket))
|
|
if min(max(bracket) - alpha, alpha - min(bracket)) < eps:
|
|
# interpolation close to boundary
|
|
if insuf_progress or alpha >= max(bracket) or alpha <= min(bracket):
|
|
# evaluate at 0.1 away from boundary
|
|
if abs(alpha - max(bracket)) < abs(alpha - min(bracket)):
|
|
alpha = max(bracket) - eps
|
|
else:
|
|
alpha = min(bracket) + eps
|
|
insuf_progress = False
|
|
else:
|
|
insuf_progress = True
|
|
else:
|
|
insuf_progress = False
|
|
# Evaluate new point
|
|
loss_new, grad_new = obj_func(xk, alpha, d)
|
|
ls_func_evals += 1
|
|
gtd_new = dot(grad_new, d)
|
|
ls_iter += 1
|
|
|
|
if (
|
|
loss_new > (loss + c1 * alpha * gtd)
|
|
or loss_new >= bracket_f[low_pos]
|
|
):
|
|
# Armijo condition not satisfied or not lower than lowest point
|
|
bracket[high_pos] = alpha
|
|
bracket_f[high_pos] = loss_new
|
|
bracket_g[high_pos] = grad_new.clone()
|
|
bracket_gtd[high_pos] = gtd_new
|
|
low_pos, high_pos = (
|
|
(0, 1) if bracket_f[0] <= bracket_f[1] else (1, 0)
|
|
)
|
|
else:
|
|
if abs(gtd_new) <= -c2 * gtd:
|
|
# Wolfe conditions satisfied
|
|
done = True
|
|
elif gtd_new * (bracket[high_pos] - bracket[low_pos]) >= 0:
|
|
# old high becomes new low
|
|
bracket[high_pos] = bracket[low_pos]
|
|
bracket_f[high_pos] = bracket_f[low_pos]
|
|
bracket_g[high_pos] = bracket_g[low_pos]
|
|
bracket_gtd[high_pos] = bracket_gtd[low_pos]
|
|
|
|
# new point becomes new low
|
|
bracket[low_pos] = alpha
|
|
bracket_f[low_pos] = loss_new
|
|
bracket_g[low_pos] = grad_new.clone()
|
|
bracket_gtd[low_pos] = gtd_new
|
|
|
|
# return stuff
|
|
alpha = bracket[low_pos]
|
|
loss_new = bracket_f[low_pos]
|
|
grad_new = bracket_g[low_pos]
|
|
return loss_new, grad_new, alpha, ls_func_evals
|
|
|
|
|
|
class LBFGS(Optimizer):
|
|
r"""
|
|
The L-BFGS is a quasi-Newton method for solving an unconstrained optimization problem over a differentiable function.
|
|
Closely related is the Newton method for minimization. Consider the iterate update formula:
|
|
|
|
.. math::
|
|
x_{k+1} = x_{k} + H_k \nabla{f_k}
|
|
|
|
If :math:`H_k` is the inverse Hessian of :math:`f` at :math:`x_k`, then it's the Newton method.
|
|
If :math:`H_k` is symmetric and positive definite, used as an approximation of the inverse Hessian, then
|
|
it's a quasi-Newton. In practice, the approximated Hessians are obtained
|
|
by only using the gradients, over either whole or part of the search
|
|
history, the former is BFGS, the latter is L-BFGS.
|
|
|
|
Reference:
|
|
Jorge Nocedal, Stephen J. Wright, Numerical Optimization, Second Edition, 2006. pp179: Algorithm 7.5 (L-BFGS).
|
|
|
|
Args:
|
|
learning_rate (float, optional): learning rate .The default value is 1.
|
|
max_iter (int, optional): maximal number of iterations per optimization step.
|
|
The default value is 20.
|
|
max_eval (int|None, optional): maximal number of function evaluations per optimization
|
|
step. The default value is max_iter * 1.25.
|
|
tolerance_grad (float, optional): termination tolerance on first order optimality
|
|
The default value is 1e-5.
|
|
tolerance_change (float, optional): termination tolerance on function
|
|
value/parameter changes. The default value is 1e-9.
|
|
history_size (int, optional): update history size. The default value is 100.
|
|
line_search_fn (string|None, optional): either 'strong_wolfe' or None. The default value is strong_wolfe.
|
|
parameters (list|tuple|None, optional): List/Tuple of ``Tensor`` names to update to minimize ``loss``. \
|
|
This parameter is required in dygraph mode. The default value is None.
|
|
weight_decay (int|float|WeightDecayRegularizer|None, optional): The strategy of regularization. \
|
|
It can be a int or float value as coeff of L2 regularization or \
|
|
:ref:`api_paddle_regularizer_L1Decay`, :ref:`api_paddle_regularizer_L2Decay`.
|
|
If a parameter has set regularizer using :ref:`api_paddle_ParamAttr` already, \
|
|
the regularization setting here in optimizer will be ignored for this parameter. \
|
|
Otherwise, the regularization setting here in optimizer will take effect. \
|
|
Default None, meaning there is no regularization.
|
|
grad_clip (GradientClipBase|None, optional): Gradient clipping strategy, it's an instance of \
|
|
some derived class of ``GradientClipBase`` . There are three clipping strategies \
|
|
( :ref:`api_paddle_nn_ClipGradByGlobalNorm` , :ref:`api_paddle_nn_ClipGradByNorm` , \
|
|
:ref:`api_paddle_nn_ClipGradByValue` ). Default None, meaning there is no gradient clipping.
|
|
name (str|None, optional): Normally there is no need for user to set this property.
|
|
For more information, please refer to :ref:`api_guide_Name`.
|
|
The default value is None.
|
|
|
|
Return:
|
|
loss (Tensor): the final loss of closure.
|
|
|
|
Examples:
|
|
.. code-block:: pycon
|
|
|
|
>>> import paddle
|
|
>>> import numpy as np
|
|
|
|
>>> paddle.disable_static()
|
|
>>> np.random.seed(0)
|
|
>>> np_w = np.random.rand(1).astype(np.float32)
|
|
>>> np_x = np.random.rand(1).astype(np.float32)
|
|
|
|
>>> inputs = [np.random.rand(1).astype(np.float32) for i in range(10)]
|
|
>>> # y = 2x
|
|
>>> targets = [2 * x for x in inputs]
|
|
|
|
>>> class Net(paddle.nn.Layer):
|
|
... def __init__(self):
|
|
... super().__init__()
|
|
... w = paddle.to_tensor(np_w)
|
|
... self.w = paddle.create_parameter(shape=w.shape, dtype=w.dtype, default_initializer=paddle.nn.initializer.Assign(w))
|
|
...
|
|
... def forward(self, x):
|
|
... return self.w * x
|
|
...
|
|
>>> net = Net()
|
|
>>> opt = paddle.optimizer.LBFGS(learning_rate=1, max_iter=1, max_eval=None, tolerance_grad=1e-07, tolerance_change=1e-09, history_size=100, line_search_fn='strong_wolfe', parameters=net.parameters())
|
|
>>> def train_step(inputs, targets):
|
|
... def closure():
|
|
... outputs = net(inputs)
|
|
... loss = paddle.nn.functional.mse_loss(outputs, targets)
|
|
... print('loss: ', loss.item())
|
|
... opt.clear_grad()
|
|
... loss.backward()
|
|
... return loss
|
|
... opt.step(closure)
|
|
...
|
|
>>> for input_np, target_np in zip(inputs, targets):
|
|
... input = paddle.to_tensor(input_np)
|
|
... target = paddle.to_tensor(target_np)
|
|
... train_step(input, target)
|
|
"""
|
|
|
|
def __init__(
|
|
self,
|
|
learning_rate: float = 1.0,
|
|
max_iter: int = 20,
|
|
max_eval: int | None = None,
|
|
tolerance_grad: float = 1e-7,
|
|
tolerance_change: float = 1e-9,
|
|
history_size: int = 100,
|
|
line_search_fn: str | None = None,
|
|
parameters: Sequence[Tensor] | Sequence[_ParameterConfig] | None = None,
|
|
weight_decay: float | WeightDecayRegularizer | None = None,
|
|
grad_clip: GradientClipBase | None = None,
|
|
name: str | None = None,
|
|
) -> None:
|
|
check_tf32_override()
|
|
|
|
if max_eval is None:
|
|
max_eval = max_iter * 5 // 4
|
|
|
|
self.learning_rate = learning_rate
|
|
self.max_iter = max_iter
|
|
self.max_eval = max_eval
|
|
self.tolerance_grad = tolerance_grad
|
|
self.tolerance_change = tolerance_change
|
|
self.history_size = history_size
|
|
self.line_search_fn = line_search_fn
|
|
|
|
if isinstance(parameters, paddle.Tensor):
|
|
raise TypeError(
|
|
"parameters argument given to the optimizer should be "
|
|
"an iterable of Tensors or dicts, but got " + type(parameters)
|
|
)
|
|
|
|
self.state = defaultdict(dict)
|
|
|
|
super().__init__(
|
|
learning_rate=1.0,
|
|
parameters=parameters,
|
|
weight_decay=weight_decay,
|
|
grad_clip=grad_clip,
|
|
name=name,
|
|
)
|
|
|
|
if not isinstance(self._parameter_list[0], dict):
|
|
self._params = self._parameter_list
|
|
else:
|
|
for idx, param_group in enumerate(self._param_groups):
|
|
self._params = param_group['params']
|
|
|
|
self._numel_cache = None
|
|
|
|
def state_dict(self) -> _LbfgsStateDict:
|
|
r"""Returns the state of the optimizer as a :class:`dict`.
|
|
|
|
Return:
|
|
state, a dict holding current optimization state. Its content
|
|
differs between optimizer classes.
|
|
|
|
Examples:
|
|
.. code-block:: pycon
|
|
|
|
>>> import paddle
|
|
|
|
>>> paddle.disable_static()
|
|
|
|
>>> net = paddle.nn.Linear(10, 10)
|
|
>>> opt = paddle.optimizer.LBFGS(
|
|
... learning_rate=1,
|
|
... max_iter=1,
|
|
... max_eval=None,
|
|
... tolerance_grad=1e-07,
|
|
... tolerance_change=1e-09,
|
|
... history_size=100,
|
|
... line_search_fn='strong_wolfe',
|
|
... parameters=net.parameters(),
|
|
>>> )
|
|
|
|
>>> def train_step(inputs, targets):
|
|
... def closure():
|
|
... outputs = net(inputs)
|
|
... loss = paddle.nn.functional.mse_loss(outputs, targets)
|
|
... opt.clear_grad()
|
|
... loss.backward()
|
|
... return loss
|
|
...
|
|
... opt.step(closure)
|
|
>>> inputs = paddle.rand([10, 10], dtype="float32")
|
|
>>> targets = paddle.to_tensor([2 * x for x in inputs])
|
|
|
|
>>> n_iter = 0
|
|
>>> while n_iter < 20:
|
|
... loss = train_step(inputs, targets)
|
|
... n_iter = opt.state_dict()["state"]["func_evals"]
|
|
... print("n_iter:", n_iter)
|
|
"""
|
|
|
|
packed_state = {}
|
|
for k, v in self.state.items():
|
|
packed_state.update({k: v})
|
|
|
|
return {'state': packed_state}
|
|
|
|
def _numel(self) -> int:
|
|
# compute the number of all parameters
|
|
if self._numel_cache is None:
|
|
self._numel_cache = reduce(
|
|
lambda total, p: total + p.numel(), self._params, 0
|
|
)
|
|
return self._numel_cache
|
|
|
|
# flatten grad of all parameters
|
|
def _gather_flat_grad(self):
|
|
views = []
|
|
for p in self._params:
|
|
if p.grad is None:
|
|
view = paddle.zeros_like(p).reshape([-1])
|
|
else:
|
|
view = p.grad.reshape([-1])
|
|
views.append(view)
|
|
return paddle.concat(views, axis=0)
|
|
|
|
# compute xk = xk + alpha * direction
|
|
def _add_grad(self, alpha, direction):
|
|
offset = 0
|
|
for p in self._params:
|
|
numel = reduce(lambda x, y: x * y, p.shape) if p.shape != [] else 1
|
|
p = paddle.assign(
|
|
p.add(
|
|
direction[offset : offset + numel].reshape(p.shape) * alpha
|
|
),
|
|
p,
|
|
)
|
|
offset += numel
|
|
assert offset == self._numel()
|
|
|
|
def _clone_param(self):
|
|
return [p.clone() for p in self._params]
|
|
|
|
def _set_param(self, params_data):
|
|
for p, pdata in zip(self._params, params_data):
|
|
paddle.assign(pdata, p)
|
|
|
|
def _directional_evaluate(self, closure, x, alpha, d):
|
|
self._add_grad(alpha, d)
|
|
loss = float(closure())
|
|
flat_grad = self._gather_flat_grad()
|
|
self._set_param(x)
|
|
return loss, flat_grad
|
|
|
|
@framework.non_static_only
|
|
def step(self, closure) -> Tensor:
|
|
"""Performs a single optimization step.
|
|
|
|
Args:
|
|
closure (callable): A closure that reevaluates the model
|
|
and returns the loss.
|
|
|
|
Examples:
|
|
.. code-block:: pycon
|
|
|
|
>>> import paddle
|
|
|
|
>>> paddle.disable_static()
|
|
|
|
>>> inputs = paddle.rand([10, 10], dtype="float32")
|
|
>>> targets = paddle.to_tensor([2 * x for x in inputs])
|
|
|
|
>>> net = paddle.nn.Linear(10, 10)
|
|
>>> opt = paddle.optimizer.LBFGS(
|
|
... learning_rate=1,
|
|
... max_iter=1,
|
|
... max_eval=None,
|
|
... tolerance_grad=1e-07,
|
|
... tolerance_change=1e-09,
|
|
... history_size=100,
|
|
... line_search_fn='strong_wolfe',
|
|
... parameters=net.parameters(),
|
|
>>> )
|
|
|
|
>>> def closure():
|
|
... outputs = net(inputs)
|
|
... loss = paddle.nn.functional.mse_loss(outputs, targets)
|
|
... print("loss:", loss.item())
|
|
... opt.clear_grad()
|
|
... loss.backward()
|
|
... return loss
|
|
>>> opt.step(closure)
|
|
"""
|
|
|
|
with paddle.no_grad():
|
|
# Make sure the closure is always called with grad enabled
|
|
closure = paddle.enable_grad()(closure)
|
|
|
|
learning_rate = self.learning_rate
|
|
max_iter = self.max_iter
|
|
max_eval = self.max_eval
|
|
tolerance_grad = self.tolerance_grad
|
|
tolerance_change = self.tolerance_change
|
|
line_search_fn = self.line_search_fn
|
|
history_size = self.history_size
|
|
state = self.state
|
|
state.setdefault('func_evals', 0)
|
|
state.setdefault('n_iter', 0)
|
|
|
|
# evaluate initial f(x) and df/dx
|
|
orig_loss = closure()
|
|
loss = float(orig_loss)
|
|
|
|
current_evals = 1
|
|
state['func_evals'] += 1
|
|
|
|
flat_grad = self._gather_flat_grad()
|
|
opt_cond = flat_grad.abs().max() <= tolerance_grad
|
|
|
|
# optimal condition
|
|
if opt_cond:
|
|
return orig_loss
|
|
|
|
# tensors cached in state (for tracing)
|
|
d = state.get('d')
|
|
alpha = state.get('alpha')
|
|
old_yk = state.get('old_yk')
|
|
old_sk = state.get('old_sk')
|
|
ro = state.get('ro')
|
|
H_diag = state.get('H_diag')
|
|
prev_flat_grad = state.get('prev_flat_grad')
|
|
prev_loss = state.get('prev_loss')
|
|
|
|
n_iter = 0
|
|
# optimize for a max of max_iter iterations
|
|
while n_iter < max_iter:
|
|
# keep track of nb of iterations
|
|
n_iter += 1
|
|
state['n_iter'] += 1
|
|
|
|
############################################################
|
|
# compute gradient descent direction
|
|
############################################################
|
|
if state['n_iter'] == 1:
|
|
d = flat_grad.neg()
|
|
old_yk = []
|
|
old_sk = []
|
|
ro = []
|
|
H_diag = paddle.to_tensor(1.0, dtype=orig_loss.dtype)
|
|
else:
|
|
# do lbfgs update (update memory)
|
|
y = flat_grad.subtract(prev_flat_grad)
|
|
s = d.multiply(paddle.to_tensor(alpha, dtype=d.dtype))
|
|
ys = dot(y, s)
|
|
if ys > 1e-10:
|
|
# updating memory
|
|
if len(old_yk) == history_size:
|
|
# shift history by one (limited-memory)
|
|
old_yk.pop(0)
|
|
old_sk.pop(0)
|
|
ro.pop(0)
|
|
|
|
# store new direction/step
|
|
old_yk.append(y)
|
|
old_sk.append(s)
|
|
ro.append(1.0 / ys)
|
|
|
|
# update scale of initial Hessian approximation
|
|
H_diag = ys / dot(y, y) # (y*y)
|
|
|
|
# compute the approximate (L-BFGS) inverse Hessian
|
|
# multiplied by the gradient
|
|
num_old = len(old_yk)
|
|
|
|
if 'al' not in state:
|
|
state['al'] = [None] * history_size
|
|
al = state['al']
|
|
|
|
# iteration in L-BFGS loop collapsed to use just one buffer
|
|
q = flat_grad.neg()
|
|
for i in range(num_old - 1, -1, -1):
|
|
al[i] = dot(old_sk[i], q) * ro[i]
|
|
paddle.assign(q.add(old_yk[i] * (-al[i])), q)
|
|
|
|
# multiply by initial Hessian
|
|
# r/d is the final direction
|
|
d = r = paddle.multiply(q, H_diag)
|
|
for i in range(num_old):
|
|
be_i = dot(old_yk[i], r) * ro[i]
|
|
paddle.assign(r.add(old_sk[i] * (al[i] - be_i)), r)
|
|
|
|
if prev_flat_grad is None:
|
|
prev_flat_grad = flat_grad.clone()
|
|
else:
|
|
paddle.assign(flat_grad, prev_flat_grad)
|
|
prev_loss = loss
|
|
|
|
############################################################
|
|
# compute step length
|
|
############################################################
|
|
# reset initial guess for step size
|
|
if state['n_iter'] == 1:
|
|
alpha = (
|
|
min(1.0, 1.0 / flat_grad.abs().sum()) * learning_rate
|
|
)
|
|
else:
|
|
alpha = learning_rate
|
|
|
|
# directional derivative
|
|
gtd = dot(flat_grad, d)
|
|
|
|
# directional derivative is below tolerance
|
|
if gtd > -tolerance_change:
|
|
break
|
|
|
|
# optional line search: user function
|
|
ls_func_evals = 0
|
|
if line_search_fn is not None:
|
|
# perform line search, using user function
|
|
if line_search_fn != "strong_wolfe":
|
|
raise RuntimeError("only 'strong_wolfe' is supported")
|
|
else:
|
|
x_init = self._clone_param()
|
|
|
|
def obj_func(x, alpha, d):
|
|
return self._directional_evaluate(
|
|
closure, x, alpha, d
|
|
)
|
|
|
|
loss, flat_grad, alpha, ls_func_evals = _strong_wolfe(
|
|
obj_func, x_init, alpha, d, loss, flat_grad, gtd
|
|
)
|
|
self._add_grad(alpha, d)
|
|
opt_cond = flat_grad.abs().max() <= tolerance_grad
|
|
else:
|
|
# no line search, simply move with fixed-step
|
|
self._add_grad(alpha, d)
|
|
if n_iter != max_iter:
|
|
with paddle.enable_grad():
|
|
loss = float(closure())
|
|
flat_grad = self._gather_flat_grad()
|
|
opt_cond = flat_grad.abs().max() <= tolerance_grad
|
|
ls_func_evals = 1
|
|
|
|
# update func eval
|
|
current_evals += ls_func_evals
|
|
state['func_evals'] += ls_func_evals
|
|
|
|
# optimal condition
|
|
if opt_cond:
|
|
break
|
|
|
|
# lack of progress
|
|
if (d * alpha).abs().max() <= tolerance_change:
|
|
break
|
|
|
|
if abs(loss - prev_loss) < tolerance_change:
|
|
break
|
|
|
|
# check conditions
|
|
if current_evals >= max_eval:
|
|
break
|
|
|
|
if n_iter == max_iter:
|
|
break
|
|
|
|
state['d'] = d
|
|
state['alpha'] = alpha
|
|
state['old_yk'] = old_yk
|
|
state['old_sk'] = old_sk
|
|
state['ro'] = ro
|
|
state['H_diag'] = H_diag
|
|
state['prev_flat_grad'] = prev_flat_grad
|
|
state['prev_loss'] = prev_loss
|
|
|
|
return orig_loss
|
|
|
|
def minimize(
|
|
self, loss, startup_program=None, parameters=None, no_grad_set=None
|
|
) -> NoReturn:
|
|
"""Empty method. LBFGS optimizer does not use this way to minimize ``loss``. Please refer 'Examples' of LBFGS() above for usage."""
|
|
raise NotImplementedError(
|
|
"LBFGS optimizer does not use this way to minimize loss. Please refer 'Examples' of LBFGS() for usage."
|
|
)
|