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lbfgs.py
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lbfgs.py
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import torch
import numpy as np
def lbfgs(f, init, maxIter=50, gEps=1e-8, histSize=10, lr=1.0, clamp=False, display=False):
"""
input:
f: a function
in: value x; 1-d tensor
out: result fx, gradient g
init: a valid input for f
maxIter: ---
gEps: ---
histSize: ---
output:
x: argmin{x} f(x); 1-d tensor
"""
xk = init
fk, gk = f(xk)
H0 = 1.0
evals = 1
step = 0
stat = "LBFGS REACH MAX ITER"
alpha = list(range(histSize))
rho = []
s = []
y = []
for it in range(maxIter):
#print(len(alpha), len(rho), len(s), len(y))
if display and it%20==0:
print("LBFGS | iter:{}; loss:{:.4f}; grad:{:.4f}; step:{:.5f}".format(it, fk, np.sqrt(torch.sum((gk)**2)), step))
if clamp:
xk = xk.clamp(0, 1e7)
xSquaredNorm = torch.sum(xk * xk)
gSquaredNorm = torch.sum(gk * gk)
if gSquaredNorm < (gEps**2) * xSquaredNorm:
stat = "LBFGS BELOW GRADIENT EPS"
return xk, stat
z = -gk
maxIdx = min(it, histSize)
for i in range(maxIdx):
alpha[i] = s[i].dot(z) * rho[i]
z -= alpha[i] * y[i]
z *= H0
for i in range(maxIdx-1, -1, -1):
beta = rho[i] * y[i].dot(z)
z += s[i] * (alpha[i] - beta)
fkm1, gkm1 = fk, gk
step, stat_ls, args = linesearch(xk.clone(), z, f, fk, gk.clone(), fkm1,gkm1.clone(), 10000, lr)
if step is None:
xk, fk, gk = args
return xk, stat_ls
else:
xk, fk, gk = args
"""
step = 1.0
xk += step * z
fk, gk = f(xk)
#if (gk==gkm1).any():
# print("error!")
"""
if it >= histSize:
s.pop(0)
y.pop(0)
rho.pop(0)
s.append(z * step)
y.append(gk - gkm1)
yDots = y[-1].dot(s[-1])
try:
rho.append(1.0 / yDots)
except ZeroDivisionError:
print(y[-1], s[-1])
return xk, "Zero division"
yNorm2 = y[-1].dot(y[-1])
if yNorm2 > 1e-5:
H0 = yDots / yNorm2
return xk, stat
def linesearch(xk, z, f, fk, gk, fkm1, gkm1, maxEvals, lr):
"""
"""
c1 = 1e-4
c2 = 0.9
evals = 0
alpha_0 = 0.0
phi_0 = fkm1
phi_prime_0 = z.dot(gk)
if phi_prime_0 >= 0.0:
stat = "LINE SEARCH FAILED"
return None, stat, [xk, fk, gk]
alpha_max = 1e8
alpha = lr
alpha_old = 0.0
alpha_cor = lr
second_iter = False
while True:
xk += (alpha - alpha_old) * z
fk, gk = f(xk)
evals += 1
phi_alpha = fk
phi_prime_alpha = z.dot(gk)
armijo_violated = (phi_alpha > phi_0 + c1 * alpha * phi_prime_0 or (second_iter and phi_alpha >= phi_0))
strong_wolfe = (torch.abs(phi_prime_alpha) <= -c2 * phi_prime_0)
if (not armijo_violated) and strong_wolfe:
stat = "LINE SEARCH DONE"
return alpha, stat, [xk, fk, gk]
if evals > maxEvals:
stat = "LINE SEARCH REACH MAX EVALS"
return None, stat, [xk, fk, gk]
if armijo_violated or phi_prime_alpha >= 0:
if armijo_violated:
alpha_low = alpha_0
alpha_high = alpha
phi_low = phi_0
phi_high = phi_alpha
phi_prime_low = phi_prime_0
phi_prime_high = phi_prime_alpha
else:
alpha_low = alpha
alpha_high = alpha_0
phi_low = phi_alpha
phi_high = phi_0
phi_prime_low = phi_prime_alpha
phi_prime_high = phi_prime_0
alpha_old = alpha;
alpha = 0.5 * (alpha_low + alpha_high)
alpha += (phi_high - phi_low) / (phi_prime_low - phi_prime_high)
if (alpha < min(alpha_low, alpha_high) or alpha > max(alpha_low, alpha_high)):
alpha = 0.5 * (alpha_low + alpha_high)
alpha_cor = alpha - alpha_old
break
alpha_new = alpha + 4 * (alpha - alpha_old)
alpha_old = alpha
alpha = alpha_new
alpha_cor = alpha - alpha_old
if alpha > alpha_max:
stat = "LINE SEARCH FAILED"
return None, stat, [xk, fk, gk]
second_iter = True
tries = 0
minTries = 10
while True:
tries += 1
"""
alpha_old = alpha
alpha = 0.5 * (alpha_low + alpha_high)
try:
alpha += (phi_high - phi_low) / (phi_prime_low - phi_prime_high)
except ZeroDivisionError:
print(alpha, phi_prime_low, phi_prime_high)
if (alpha < alpha_low and alpha > alpha_high):
alpha = 0.5 * (alpha_low + alpha_high)
"""
xk += alpha_cor * z
fk, gk = f(xk)
evals += 1
phi_j = fk
phi_prime_j = z.dot(gk)
armijo_violated = (phi_j > phi_0 + c1 * alpha * phi_prime_0 or phi_j >= phi_low)
strong_wolfe = (torch.abs(phi_prime_j) <= -c2 * phi_prime_0);
if (not armijo_violated) and strong_wolfe:
stat = "LINE SEARCH DONE"
return alpha, stat, [xk, fk, gk]
elif np.abs(alpha_high - alpha_low) < 1e-5 and tries > minTries:
stat = "LINE SEARCH FAILED"
return None, stat, [xk, fk, gk]
elif armijo_violated:
alpha_high = alpha
phi_high = phi_j
phi_prime_high = phi_prime_j
else:
if (phi_prime_j * (alpha_high - alpha_low) >= 0):
alpha_high = alpha_low
phi_high = phi_low
phi_prime_high = phi_prime_low
alpha_low = alpha
phi_low = phi_j
phi_prime_low = phi_prime_j
alpha = 0.5 * (alpha_low + alpha_high)
alpha += (phi_high - phi_low) / (phi_prime_low - phi_prime_high)
if (alpha < min(alpha_low, alpha_high) or alpha > max(alpha_low, alpha_high)):
alpha = 0.5 * (alpha_low + alpha_high)
alpha_cor = alpha - alpha_old
if evals >= maxEvals:
stat = "LINE SEARCH REACHED MAX EVALS"
return None, stat, [xk, fk, gk]