# Copyright 2021 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# https://www.apache.org/licenses/LICENSE-2.0
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"""Nonlinear conjugate gradient algorithm."""
import warnings
from dataclasses import dataclass
from typing import Any, Callable, NamedTuple, Optional
import jax
import jax.numpy as jnp
from jaxopt._src import base
from jaxopt._src.linesearch_util import _init_stepsize
from jaxopt._src.linesearch_util import _setup_linesearch
from jaxopt._src.tree_util import tree_single_dtype, get_real_dtype
from jaxopt.tree_util import tree_add_scalar_mul
from jaxopt.tree_util import tree_div
from jaxopt.tree_util import tree_l2_norm
from jaxopt.tree_util import tree_scalar_mul
from jaxopt.tree_util import tree_sub
from jaxopt.tree_util import tree_vdot_real
from jaxopt.tree_util import tree_conj
class NonlinearCGState(NamedTuple):
"""Named tuple containing state information."""
iter_num: int
stepsize: float
error: float
value: float
grad: Any
descent_direction: Any
aux: Optional[Any] = None
num_fun_eval: int = 0
num_grad_eval: int = 0
num_linesearch_iter: int = 0
[docs]@dataclass(eq=False)
class NonlinearCG(base.IterativeSolver):
"""Nonlinear conjugate gradient solver.
Supports complex variables, see second reference.
Attributes:
fun: a smooth function of the form ``fun(x, *args, **kwargs)``.
value_and_grad: whether ``fun`` just returns the value (False) or both
the value and gradient (True).
has_aux: whether ``fun`` outputs auxiliary data or not.
If ``value_and_grad == False``, the output should be
``value, aux = fun(...)``.
If ``value_and_grad == True``, the output should be
``(value, aux), grad = fun(...)``.
The auxiliary outputs are stored in ``state.aux``.
maxiter: maximum number of proximal gradient descent iterations.
tol: tolerance of the stopping criterion.
method: which variant to calculate the beta parameter in Nonlinear CG.
"polak-ribiere", "fletcher-reeves", "hestenes-stiefel"
(default: "polak-ribiere")
linesearch: the type of line search to use: "backtracking" for backtracking
line search, "zoom" for zoom line search or "hager-zhang" for Hager-Zhang
line search.
linesearch_init: strategy for line-search initialization. By default, it
will use "increase", which will increased the step-size by a factor of
`increase_factor` at each iteration if the step-size is larger than
`min_stepsize`, and set it to `max_stepsize` otherwise. Other choices are
"max", that initializes the step-size to `max_stepsize` at every
iteration, and "current", that uses the step-size from the previous
iteration.
condition: Deprecated. Condition used to select the stepsize when using
backtracking linesearch.
maxls: maximum number of iterations to use in the line search.
decrease_factor: Deprecated. Factor by which to decrease the stepsize during
line search when using backtracking linesearch (default: 0.8).
increase_factor: factor by which to increase the stepsize during line search
(default: 1.2).
max_stepsize: upper bound on stepsize.
min_stepsize: lower bound on stepsize.
implicit_diff: whether to enable implicit diff or autodiff of unrolled
iterations.
implicit_diff_solve: the linear system solver to use.
jit: whether to JIT-compile the optimization loop (default: "auto").
unroll: whether to unroll the optimization loop (default: "auto").
verbose: whether to print error on every iteration or not.
Warning: verbose=True will automatically disable jit.
References:
Jorge Nocedal and Stephen Wright.
Numerical Optimization, second edition.
Algorithm 5.4 (page 121).
Laurent Sorber, Marc van Barel, and Lieven de Lathauwer.
Unconstrained Optimization of Real Functions in Complex Variables.
SIAM J. Optim., Vol. 22, No. 3, pp. 879-898
"""
fun: Callable
value_and_grad: bool = False
has_aux: bool = False
maxiter: int = 100
tol: float = 1e-3
method: str = "polak-ribiere" # same as SciPy
linesearch: str = "zoom"
linesearch_init: str = "increase"
condition: Any = None # deprecated in v0.8
maxls: int = 15
decrease_factor: Any = None # deprecated in v0.8
increase_factor: float = 1.2
max_stepsize: float = 1.0
# FIXME: should depend on whether float32 or float64 is used.
min_stepsize: float = 1e-6
implicit_diff: bool = True
implicit_diff_solve: Optional[Callable] = None
jit: base.AutoOrBoolean = "auto"
unroll: base.AutoOrBoolean = "auto"
verbose: int = 0
[docs] def init_state(self,
init_params: Any,
*args,
**kwargs) -> NonlinearCGState:
"""Initialize the solver state.
Args:
init_params: pytree containing the initial parameters.
*args: additional positional arguments to be passed to ``fun``.
**kwargs: additional keyword arguments to be passed to ``fun``.
Returns:
state
"""
(value, aux), grad = self._value_and_grad_with_aux(init_params,
*args,
**kwargs)
dtype = tree_single_dtype(init_params)
realdtype = get_real_dtype(dtype)
return NonlinearCGState(iter_num=jnp.asarray(0),
stepsize=jnp.asarray(
self.max_stepsize, dtype=realdtype),
error=jnp.asarray(jnp.inf, dtype=realdtype),
value=value,
grad=grad,
descent_direction=tree_scalar_mul(
-1.0, tree_conj(grad)),
aux=aux,
num_fun_eval=jnp.asarray(1, base.NUM_EVAL_DTYPE),
num_grad_eval=jnp.asarray(1, base.NUM_EVAL_DTYPE),
num_linesearch_iter=jnp.array(
0, base.NUM_EVAL_DTYPE)
)
[docs] def update(self,
params: Any,
state: NonlinearCGState,
*args,
**kwargs) -> base.OptStep:
"""Performs one iteration of Fletcher-Reeves Algorithm.
Args:
params: pytree containing the parameters.
state: named tuple containing the solver state.
*args: additional positional arguments to be passed to ``fun``.
**kwargs: additional keyword arguments to be passed to ``fun``.
Returns:
(params, state)
"""
eps = 1e-6
value = state.value
grad = state.grad
descent_direction = state.descent_direction
# Kept choice of no descent direction for backtracking line-search
# FIXME: should discuss why it was the case
if self.linesearch == "backtracking":
ls_descent_direction = None
else:
ls_descent_direction = descent_direction
init_stepsize = _init_stepsize(
self.linesearch_init,
self.max_stepsize,
self.min_stepsize,
self.increase_factor,
state.stepsize,
)
new_stepsize, ls_state = self.run_ls(
init_stepsize,
params,
value,
grad,
ls_descent_direction,
args,
kwargs,
)
new_params = ls_state.params
new_value = ls_state.value
new_grad = ls_state.grad
new_aux = ls_state.aux
new_num_fun_eval = state.num_fun_eval + ls_state.num_fun_eval
new_num_grad_eval = state.num_grad_eval + ls_state.num_grad_eval
new_num_linesearch_iter = state.num_linesearch_iter + ls_state.iter_num
if self.method == "polak-ribiere":
# See Numerical Optimization, second edition, equation (5.44).
gTg = tree_vdot_real(grad, grad)
gTg = jnp.where(gTg >= eps, gTg, eps)
new_beta = tree_vdot_real(
tree_conj(tree_sub(new_grad, grad)), tree_conj(new_grad)) / gTg
new_beta = jax.nn.relu(new_beta)
elif self.method == "fletcher-reeves":
# See Numerical Optimization, second edition, equation (5.41a).
gTg = tree_vdot_real(grad, grad)
gTg = jnp.where(gTg >= eps, gTg, eps)
new_beta = tree_vdot_real(new_grad, new_grad) / gTg
new_beta = jax.nn.relu(new_beta)
elif self.method == "hestenes-stiefel":
# See Numerical Optimization, second edition, equation (5.45).
grad_diff = tree_sub(new_grad, grad)
dTg = tree_vdot_real(tree_conj(grad_diff), descent_direction)
dTg = jnp.where(dTg >= eps, dTg, eps)
new_beta = tree_vdot_real(
tree_conj(grad_diff), tree_conj(new_grad)) / dTg
new_beta = jax.nn.relu(new_beta)
else:
raise ValueError("method argument should be either 'polak-ribiere', "
"'fletcher-reeves', or 'hestenes-stiefel'.")
new_descent_direction = tree_add_scalar_mul(tree_scalar_mul(-1, tree_conj(new_grad)),
new_beta,
descent_direction)
error = tree_l2_norm(grad)
realdtype = state.error.dtype
new_state = NonlinearCGState(iter_num=state.iter_num + 1,
stepsize=jnp.asarray(
new_stepsize, dtype=realdtype),
error=jnp.asarray(error, dtype=realdtype),
value=new_value,
grad=new_grad,
descent_direction=new_descent_direction,
aux=new_aux,
num_fun_eval=new_num_fun_eval,
num_grad_eval=new_num_grad_eval,
num_linesearch_iter=new_num_linesearch_iter)
return base.OptStep(params=new_params, state=new_state)
[docs] def optimality_fun(self, params, *args, **kwargs):
"""Optimality function mapping compatible with ``@custom_root``."""
return self._grad_fun(params, *args, **kwargs)
def _value_and_grad_fun(self, params, *args, **kwargs):
(value, _), grad = self._value_and_grad_with_aux(params, *args, **kwargs)
return value, grad
def _grad_fun(self, params, *args, **kwargs):
return self._value_and_grad_fun(params, *args, **kwargs)[1]
def __post_init__(self):
_, _, self._value_and_grad_with_aux = base._make_funs_with_aux(
fun=self.fun, value_and_grad=self.value_and_grad, has_aux=self.has_aux
)
self.reference_signature = self.fun
jit, unroll = self._get_loop_options()
linesearch_solver = _setup_linesearch(
linesearch=self.linesearch,
fun=self._value_and_grad_with_aux,
value_and_grad=True,
has_aux=True,
maxlsiter=self.maxls,
max_stepsize=self.max_stepsize,
jit=jit,
unroll=unroll,
verbose=self.verbose
)
self.run_ls = linesearch_solver.run
if self.condition is not None:
warnings.warn("Argument condition is deprecated", DeprecationWarning)
if self.decrease_factor is not None:
warnings.warn(
"Argument decrease_factor is deprecated", DeprecationWarning
)