class NaiveCONESTA(bases.ExplicitAlgorithm,
bases.IterativeAlgorithm,
bases.InformationAlgorithm):
"""A naïve implementation of COntinuation with NEsterov smoothing in a
Soft-Thresholding Algorithm, or CONESTA for short.
Parameters
----------
mu_start : Non-negative float. An optional initial value of mu.
mu_min : Non-negative float. A "very small" mu to use when computing
the stopping criterion.
tau : Float, 0 < tau < 1. The rate at which eps is decreasing. Default
is 0.5.
eps : Positive float. Tolerance for the stopping criterion.
info : List or tuple of utils.consts.Info. What, if any, extra run
information should be stored. Default is an empty list, which means
that no run information is computed nor returned.
max_iter : Non-negative integer. Maximum allowed number of iterations.
min_iter : Non-negative integer less than or equal to max_iter. Minimum
number of iterations that must be performed. Default is 1.
"""
INTERFACES = [nesterov_properties.NesterovFunction,
properties.Gradient,
properties.StepSize,
properties.ProximalOperator,
properties.Continuation]
INFO_PROVIDED = [Info.ok,
Info.num_iter,
Info.time,
Info.fvalue,
Info.mu,
Info.converged]
def __init__(self, mu_start=None, mu_min=consts.TOLERANCE,
tau=0.5,
eps=consts.TOLERANCE,
info=[], max_iter=10000, min_iter=1):
super(NaiveCONESTA, self).__init__(info=info,
max_iter=max_iter,
min_iter=min_iter)
self.mu_start = mu_start
self.mu_min = mu_min
self.tau = tau
self.eps = eps
# Copy the allowed info keys for FISTA.
fista_info = list()
for nfo in self.info_copy():
if nfo in FISTA.INFO_PROVIDED:
fista_info.append(nfo)
if Info.num_iter not in fista_info:
fista_info.append(Info.num_iter)
self.algorithm = FISTA(eps=eps, max_iter=max_iter, min_iter=min_iter,
info=fista_info)
self.num_iter = 0
@bases.force_reset
@bases.check_compatibility
def run(self, function, beta):
# self.info.clear()
if self.info_requested(Info.ok):
self.info_set(Info.ok, False)
if self.mu_start is None:
mu = function.estimate_mu(beta)
else:
mu = self.mu_start
# We use 2x as in Chen et al. (2012).
eps = 2.0 * function.eps_max(mu)
function.set_mu(self.mu_min)
tmin = function.step(beta)
function.set_mu(mu)
if self.info_requested(Info.mu):
mu = [mu]
if self.info_requested(Info.time):
t = []
if self.info_requested(Info.fvalue):
f = []
if self.info_requested(Info.converged):
self.info_set(Info.converged, False)
i = 0
while True:
tnew = function.step(beta)
self.algorithm.set_params(step=tnew, eps=eps,
max_iter=self.max_iter - self.num_iter)
# self.fista_info.clear()
beta = self.algorithm.run(function, beta)
self.num_iter += self.algorithm.num_iter
if Info.time in self.algorithm.info:
tval = self.algorithm.info_get(Info.time)
if Info.fvalue in self.algorithm.info:
fval = self.algorithm.info_get(Info.fvalue)
if self.info_requested(Info.time):
t = t + tval
if self.info_requested(Info.fvalue):
f = f + fval
old_mu = function.set_mu(self.mu_min)
# Take one ISTA step for use in the stopping criterion.
beta_tilde = function.prox(beta - tmin * function.grad(beta),
tmin)
function.set_mu(old_mu)
if (1.0 / tmin) * maths.norm(beta - beta_tilde) < self.eps:
if self.info_requested(Info.converged):
self.info_set(Info.converged, True)
break
if self.num_iter >= self.max_iter:
break
eps = max(self.tau * eps, consts.TOLERANCE)
# if eps <= consts.TOLERANCE:
# break
if self.info_requested(Info.mu):
mu_new = max(self.mu_min, self.tau * mu[-1])
mu = mu + [mu_new] * len(fval)
else:
mu_new = max(self.mu_min, self.tau * mu)
mu = mu_new
print "eps:", eps, ", mu:", mu_new
function.set_mu(mu_new)
i = i + 1
if self.info_requested(Info.num_iter):
self.info_set(Info.num_iter, i + 1)
if self.info_requested(Info.time):
self.info_set(Info.time, t)
if self.info_requested(Info.fvalue):
self.info_set(Info.fvalue, f)
if self.info_requested(Info.mu):
self.info_set(Info.mu, mu)
if self.info_requested(Info.ok):
self.info_set(Info.ok, True)
return beta
def run(self, function, beta):
# Copy the allowed info keys for FISTA.
fista_info = list()
for nfo in self.info_copy():
if nfo in FISTA.INFO_PROVIDED:
fista_info.append(nfo)
# if not self.fista_info.allows(Info.num_iter):
# self.fista_info.add_key(Info.num_iter)
# Create the inner algorithm.
algorithm = FISTA(eps=self.eps,
max_iter=self.max_iter, min_iter=self.min_iter,
info=fista_info)
if self.info_requested(Info.ok):
self.info_set(Info.ok, False)
if self.mu_start is None:
mu = [function.estimate_mu(beta)]
else:
mu = [self.mu_start]
function.set_mu(self.mu_min)
tmin = function.step(beta)
function.set_mu(mu[0])
max_eps = function.eps_max(mu[0])
G = min(max_eps, function.eps_opt(mu[0]))
if self.info_requested(Info.time):
t = []
if self.info_requested(Info.fvalue):
f = []
if self.info_requested(Info.gap):
Gval = []
if self.info_requested(Info.converged):
self.info_set(Info.converged, False)
i = 0
while True:
stop = False
tnew = function.step(beta)
eps_plus = min(max_eps, function.eps_opt(mu[-1]))
# print "current iterations: ", self.num_iter, \
# ", iterations left: ", self.max_iter - self.num_iter
algorithm.set_params(step=tnew, eps=eps_plus,
max_iter=self.max_iter - self.num_iter,
conesta_stop=None)
# conesta_stop=[self.mu_min])
# self.fista_info.clear()
beta = algorithm.run(function, beta)
#print "CONESTA loop", i, "FISTA=",self.fista_info[Info.num_iter], "TOT iter:", self.num_iter
self.num_iter += algorithm.num_iter
if Info.time in algorithm.info:
tval = algorithm.info_get(Info.time)
if Info.fvalue in algorithm.info:
fval = algorithm.info_get(Info.fvalue)
self.mu_min = min(self.mu_min, mu[-1])
tmin = min(tmin, tnew)
old_mu = function.set_mu(self.mu_min)
# Take one ISTA step for use in the stopping criterion.
beta_tilde = function.prox(beta - tmin * function.grad(beta),
tmin)
function.set_mu(old_mu)
if (1.0 / tmin) * maths.norm(beta - beta_tilde) < self.eps:
if self.info_requested(Info.converged):
self.info_set(Info.converged, True)
stop = True
if self.num_iter >= self.max_iter:
stop = True
if self.info_requested(Info.time):
gap_time = utils.time_cpu()
if self.dynamic:
G_new = function.gap(beta, eps=eps_plus,
max_iter=self.max_iter - self.num_iter)
# TODO: Warn if G_new < 0.
G_new = abs(G_new) # Just in case ...
if G_new < G:
G = G_new
else:
G = self.tau * G
else: # Static
G = self.tau * G
if self.info_requested(Info.time):
gap_time = utils.time_cpu() - gap_time
tval[-1] += gap_time
t = t + tval
if self.info_requested(Info.fvalue):
f = f + fval
if self.info_requested(Info.gap):
Gval.append(G)
if (G <= consts.TOLERANCE and mu[-1] <= consts.TOLERANCE) or stop:
break
mu_new = min(mu[-1], function.mu_opt(G))
self.mu_min = min(self.mu_min, mu_new)
if self.info_requested(Info.mu):
mu = mu + [max(self.mu_min, mu_new)] * len(fval)
else:
mu.append(max(self.mu_min, mu_new))
function.set_mu(mu_new)
i = i + 1
if self.info_requested(Info.num_iter):
self.info_set(Info.num_iter, i + 1)
if self.info_requested(Info.time):
self.info_set(Info.time, t)
if self.info_requested(Info.fvalue):
self.info_set(Info.fvalue, f)
if self.info_requested(Info.gap):
self.info_set(Info.gap, Gval)
if self.info_requested(Info.mu):
self.info_set(Info.mu, mu)
if self.info_requested(Info.ok):
self.info_set(Info.ok, True)
return beta