def main():
np.random.seed(47)
n = 10000
p = 10
n_arm = 2
divide = 1
coef_ = np.array(
[np.zeros(p + int((p + 1) * p / 2)) for _ in range(int(n_arm))])
coef_[0][11] = -6.0
coef_[0][1] = 4.0
coef_[1][1] = 4.0
coef_[1][0] = -6.0
#coef_[1][11] = 4
'''
data
'''
R = 50
size = int((n + 1) / 200)
X_oracle = np.zeros(R * size).reshape(size, R)
X_low = np.zeros(R * size).reshape(size, R)
X_cross = np.zeros(R * size).reshape(size, R)
X_random = np.zeros(R * size).reshape(size, R)
for r_ in range(R):
x = np.random.uniform(-1, 1, p * n).reshape(n, p)
for j in range(n):
x[j, :] = x[j, :] / np.sqrt(np.dot(x[j, :], x[j, :])) * 2
e = np.random.normal(0, 0.05, n_arm * n).reshape(n, n_arm)
for i in range(n_arm):
coef_[i] = coef_[i] / np.sqrt(np.dot(coef_[i], coef_[i])) * 1
#print(coef_)
X = cross_gene_(x)
#print(X[0:6, 0:20])
select_cross_low = bandit_low_cross(x, e, coef_)
select_cross = bandit_high(X, e, coef_) #Consider the cross-terms
select_oracle = bandit_oracle(X, coef_)
select_random = np.random.randint(0, coef_.shape[0], n)
'''
print(select_cross[0][500:600])
print(risk_calculator(X, e, coef_, select_oracle)[10], 'oracle')
print(risk_calculator(X, e, coef_, select_cross[0])[10], 'cross')
print(risk_calculator(X, e, coef_, select_cross_low[0])[10], 'cross_low')
print(risk_calculator(X, e, coef_, select_random), 'random')
'''
X_oracle[:, r_] = risk_calculator(X, e, coef_, select_oracle)
X_low[:, r_] = risk_calculator(X, e, coef_, select_cross_low[0])
X_cross[:, r_] = risk_calculator(X, e, coef_, select_cross[0])
X_random[:, r_] = risk_calculator(X, e, coef_, select_random)
'''
Save the simulating data
'''
'''
def main():
'''
high-dimension winning case:
'''
np.random.seed(47)
n = 10000
p = 100
n_arm = 6
divide = 1
#Sparse example:
coef_high = np.array([np.zeros(p) for _ in range(int(n_arm))])
for j in range(n_arm):
#print(coef_high[j])
#print(coef_high[j][np.random.choice(range(p), 3, replace=False).astype(int)])
coef_high[j][np.random.choice(range(p), 3, replace=False).astype(int)] \
= np.random.uniform(0,10, 3)
coef_high[j] = coef_high[j] / np.sqrt(
np.dot(coef_high[j], coef_high[j]))
coef_ = coef_high
'''
data
'''
R = 50
size = int((n + 1) / 200)
X_oracle = np.zeros(R * size).reshape(size, R)
X_low = np.zeros(R * size).reshape(size, R)
X_high = np.zeros(R * size).reshape(size, R)
X_bylearning = np.zeros(R * size).reshape(size, R)
X_random = np.zeros(R * size).reshape(size, R)
for r_ in range(R):
x = np.random.uniform(-1, 1, p * n).reshape(n, p)
for j in range(n):
x[j, :] = x[j, :] / np.sqrt(np.dot(x[j, :], x[j, :])) * 2
e = np.random.normal(0, 0.05, n_arm * n).reshape(n, n_arm)
select_1 = bandit_oracle(x, coef_)
select_2 = bandit_low(x, e, coef_)
select_3 = bandit_high(x, e, coef_)
select_4 = bandit_bylearning(x, e, coef_)
select_random = np.random.randint(0, coef_.shape[0], n)
'''
print(risk_calculator(x, e, coef_, select_1))
print(risk_calculator(x, e, coef_, select_2[0]), 'low')
print(risk_calculator(x, e, coef_, select_3[0]), 'high')
print(risk_calculator(x, e, coef_, select_4[0]), 'bylearning')
print(risk_calculator(x, e, coef_, select_random), 'random')
'''
X_oracle[:, r_] = risk_calculator(x, e, coef_, select_1)
X_low[:, r_] = risk_calculator(x, e, coef_, select_2[0])
X_high[:, r_] = risk_calculator(x, e, coef_, select_3[0])
X_bylearning[:, r_] = risk_calculator(x, e, coef_, select_4[0])
X_random[:, r_] = risk_calculator(x, e, coef_, select_random)
'''
Save the simulating data
'''
'''
def main(): np.random.seed(47) n = 10000 p = 100 n_arm = 6 divide = 1 A = [np.empty((0, p), int) for _ in range(int(n_arm / divide))] for j in range(int(n_arm / divide)): A[j] = np.hstack([np.random.uniform(-5,10, p)]) A[j] = A[j] / np.sqrt(np.dot(A[j],A[j])) coef_ = np.array(A) #non-sparse example. High-dimension tends to perform badly A = [np.empty((0, p), int) for _ in range(int(n_arm / divide))] b_ = 0 for j in range(int(n_arm / divide)): A[j] = np.zeros(p) if j < int(n_arm / divide) / 3: A[j][:int(p / 3)] = np.hstack([np.random.uniform(b_,10, int(p / 3))]) elif j > int(n_arm / divide) / 3 and j <= int(n_arm / divide) / 3 * 2: A[j][int(p / 3) + 1:int(2 * p / 3)] = np.hstack([np.random.uniform(b_,10, int(2 * p / 3) - int(p / 3) - 1)]) else: A[j][int(2 * p / 3) + 1:] = np.hstack([np.random.uniform(b_,10, p - int(2 * p / 3) - 1)]) A[j] = A[j] / np.sqrt(np.dot(A[j],A[j])) coef_ = np.array(A) ''' data ''' R = 50 size = int((n+1) / 200) X_oracle = np.zeros(R * size).reshape(size, R) X_low = np.zeros(R * size).reshape(size, R) X_high = np.zeros(R * size).reshape(size, R) X_bylearning = np.zeros(R * size).reshape(size, R) X_random = np.zeros(R * size).reshape(size, R) for r_ in range(R): x = np.random.uniform(-1,1,p * n).reshape(n, p) for j in range(n): x[j,:] = x[j,:] / np.sqrt(np.dot(x[j,:], x[j,:])) * 2 e = np.random.normal(0,0.05,n_arm * n).reshape(n,n_arm) select_1 = bandit_oracle(x, coef_) select_2 = bandit_low(x, e, coef_) select_3 = bandit_high(x, e, coef_) select_4 = bandit_bylearning(x, e, coef_) select_random = np.random.randint(0, coef_.shape[0], n) ''' print(risk_calculator(x, e, coef_, select_1).round(4)) print(risk_calculator(x, e, coef_, select_2[0]).round(4), 'low') print(risk_calculator(x, e, coef_, select_3[0]).round(4), 'high') print(risk_calculator(x, e, coef_, select_4[0]).round(4), 'bylearning') print(risk_calculator(x, e, coef_, select_random), 'random') ''' X_oracle[:, r_] = risk_calculator(x, e, coef_, select_1) X_low[:, r_] = risk_calculator(x, e, coef_, select_2[0]) X_high[:, r_] = risk_calculator(x, e, coef_, select_3[0]) X_bylearning[:, r_] = risk_calculator(x, e, coef_, select_4[0]) X_random[:, r_] = risk_calculator(x, e, coef_, select_random) ''' Save the simulating data ''' '''
def main(): ''' high-dimension winning case: n = 2000 p = 200 n_arm = 6 divide = 1 x = np.random.uniform(0,1,p * n).reshape(n, p)#np.abs(np.random.normal(0,0.2,p * n).reshape(n,p)) for j in range(n): x[j,:] = x[j,:] / np.sqrt(np.dot(x[j,:], x[j,:])) * 2 e = np.random.normal(0,0.05,n_arm * n).reshape(n,n_arm) coef_high = np.array([np.zeros(p) for _ in range(int(n_arm / divide))]) for j in range(n_arm): #print(coef_high[j]) #print(coef_high[j][np.random.choice(range(p), 3, replace=False).astype(int)]) coef_high[j][np.random.choice(range(p), 3, replace=False).astype(int)] \ = np.random.uniform(0,10, 3) coef_high[j] = coef_high[j] / np.sqrt(np.dot(coef_high[j], coef_high[j])) coef_ = coef_high ''' n = 1000 p = 100 n_arm = 6 divide = 1 x = np.random.uniform(0,1,p * n).reshape(n, p) for j in range(n): x[j,:] = x[j,:] / np.sqrt(np.dot(x[j,:], x[j,:])) * 2 e = np.random.normal(0,0.05,n_arm * n).reshape(n,n_arm) ''' low, n = 2000 p = 100 n_arm = 6 divide = 1 x = np.random.uniform(0,1,p * n).reshape(n, p) for j in range(n): x[j,:] = x[j,:] / np.sqrt(np.dot(x[j,:], x[j,:])) * 2 e = np.random.normal(0,0.05,n_arm * n).reshape(n,n_arm) A = [np.empty((0, p), int) for _ in range(int(n_arm / divide))] for j in range(int(n_arm / divide)): A[j] = np.hstack([np.random.uniform(-5,10, p)]) A[j] = A[j] / np.sqrt(np.dot(A[j],A[j])) coef_ = np.array(A) ''' #non-sparse example. High-dimension tends to perform badly A = [np.empty((0, p), int) for _ in range(int(n_arm / divide))] b_ = 0 for j in range(int(n_arm / divide)): A[j] = np.zeros(p) if j < int(n_arm / divide) / 3: A[j][:int(p / 3)] = np.hstack([np.random.uniform(b_,10, int(p / 3))]) elif j > int(n_arm / divide) / 3 and j <= int(n_arm / divide) / 3 * 2: A[j][int(p / 3) + 1:int(2 * p / 3)] = np.hstack([np.random.uniform(b_,10, int(2 * p / 3) - int(p / 3) - 1)]) else: A[j][int(2 * p / 3) + 1:] = np.hstack([np.random.uniform(b_,10, p - int(2 * p / 3) - 1)]) A[j] = A[j] / np.sqrt(np.dot(A[j],A[j])) coef_ = np.array(A) #coef_ = np.array(np.vstack([A, [_ / 3 for _ in A]])) * 1 #Cool! #Sparse example: coef_high = np.array([np.zeros(p) for _ in range(int(n_arm))]) for j in range(n_arm): #print(coef_high[j]) #print(coef_high[j][np.random.choice(range(p), 3, replace=False).astype(int)]) coef_high[j][np.random.choice(range(p), 3, replace=False).astype(int)] \ = np.random.uniform(0,10, 3) coef_high[j] = coef_high[j] / np.sqrt(np.dot(coef_high[j], coef_high[j])) #coef_ = coef_high select_1 = bandit_oracle(x, coef_) select_2 = bandit_low(x, e, coef_) select_3 = bandit_high(x, e, coef_) select_4 = bandit_bylearning(x, e, coef_) print(risk_calculator(x, e, coef_, select_1)) print(risk_calculator(x, e, coef_, select_2[0]), 'low') print(risk_calculator(x, e, coef_, select_3[0]), 'high') print(risk_calculator(x, e, coef_, select_4[0]), 'bylearning') select_random = np.random.randint(0, coef_.shape[0], n) print(risk_calculator(x, e, coef_, select_random), 'random') select_random = np.random.randint(0, coef_.shape[0], n) print(risk_calculator(x, e, coef_, select_random), 'random') ''' ''' #Cross-terms; n = 1000 p = 10 n_arm = 2 divide = 1 x = np.random.uniform(0,1,p * n).reshape(n, p) for j in range(n): x[j,:] = x[j,:] / np.sqrt(np.dot(x[j,:], x[j,:])) * 2 e = np.random.normal(0,0.05,n_arm * n).reshape(n,n_arm) coef_ = np.array([np.zeros(p + int((p + 1) * p / 2)) for _ in range(int(n_arm))]) coef_[0][10] = 4.2 coef_[0][0] = -2.0 #coef_[1][1] = -2.0 coef_[1][11] = 4.0 for i in range(n_arm): coef_[i] = coef_[i] / np.sqrt(np.dot(coef_[i], coef_[i])) print(coef_) X = cross_gene_(x) select_cross_low = bandit_low_cross(x, e, coef_) select_cross = bandit_high(X, e, coef_) select_1 = bandit_oracle(X, coef_) select_random = np.random.randint(0, coef_.shape[0], n) #print(select_1) print(risk_calculator_cross(x, e, coef_, select_1), 'oracle') print(risk_calculator_cross(x, e, coef_, select_cross[0]), 'cross') print(risk_calculator_cross(x, e, coef_, select_cross_low[0]), 'cross_low') print(risk_calculator_cross(x, e, coef_, select_random), 'random')
def main():
'''
high-dimension winning case:
n = 1000
p = 100
n_arm = 3
divide = 1
x = np.random.uniform(0,1,p * n).reshape(n, p)#np.abs(np.random.normal(0,0.2,p * n).reshape(n,p))
for j in range(n):
x[j,:] = x[j,:] / np.sqrt(np.dot(x[j,:], x[j,:]))
e = np.random.normal(0,0.01,n_arm * n).reshape(n,n_arm)
coef_high = np.array([np.zeros(p) for _ in range(int(n_arm / divide))])
for j in range(n_arm):
#print(coef_high[j])
#print(coef_high[j][np.random.choice(range(p), 3, replace=False).astype(int)])
coef_high[j][np.random.choice(range(p), 3, replace=False).astype(int)] \
= np.random.uniform(0,10, 3)
coef_high[j] = coef_high[j] / np.sqrt(np.dot(coef_high[j], coef_high[j]))
coef_ = coef_high
'''
n = 2000
p = 100
n_arm = 8
divide = 1
#x = np.random.normal(0,1,p * n).reshape(n,p)
x = np.random.uniform(0, 1, p * n).reshape(n, p)
for j in range(n):
x[j, :] = x[j, :] / np.sqrt(np.dot(x[j, :], x[j, :]))
e = np.random.normal(0, 0.01, n_arm * n).reshape(n, n_arm)
'''
low, not so good an example
n = 2000
p = 100
n_arm = 8
divide = 1
x = np.random.normal(0,1,p * n).reshape(n,p)
#x = np.random.uniform(0,1,p * n).reshape(n, p)
for j in range(n):
x[j,:] = x[j,:] / np.sqrt(np.dot(x[j,:], x[j,:]))
e = np.random.normal(0,0.01,n_arm * n).reshape(n,n_arm)
A = [np.empty((0, p), int) for _ in range(int(n_arm / divide))]
for j in range(int(n_arm / divide)):
A[j] = np.hstack([np.random.uniform(-5,10, p)])
A[j] = A[j] / np.sqrt(np.dot(A[j],A[j]))
coef_ = np.array(A)
'''
#non-sparse example. High-dimension tends to perform badly
A = [np.empty((0, p), int) for _ in range(int(n_arm / divide))]
b_ = 0
for j in range(int(n_arm / divide)):
#A[j] = np.hstack([np.random.uniform(0,10, p)])
A[j] = np.zeros(p)
if j < int(n_arm / divide) / 3:
#print(A[j][:int(p / 2)])
A[j][:int(p / 3)] = np.hstack(
[np.random.uniform(b_, 10, int(p / 3))])
elif j > int(n_arm / divide) / 3 and j <= int(n_arm / divide) / 3 * 2:
A[j][int(p / 3) + 1:int(2 * p / 3)] = np.hstack(
[np.random.uniform(b_, 10,
int(2 * p / 3) - int(p / 3) - 1)])
else:
A[j][int(2 * p / 3) + 1:] = np.hstack(
[np.random.uniform(b_, 10, p - int(2 * p / 3) - 1)])
A[j] = A[j] / np.sqrt(np.dot(A[j], A[j]))
coef_ = np.array(A)
#coef_ = np.array(np.vstack([A, [_ / 3 for _ in A]])) * 1 #Cool!
coef_high = np.array([np.zeros(p) for _ in range(int(n_arm))])
for j in range(n_arm):
#print(coef_high[j])
#print(coef_high[j][np.random.choice(range(p), 3, replace=False).astype(int)])
coef_high[j][np.random.choice(range(p), 3, replace=False).astype(int)] \
= np.random.uniform(0,10, 3)
coef_high[j] = coef_high[j] / np.sqrt(
np.dot(coef_high[j], coef_high[j]))
#coef_ = coef_high
for elem in coef_:
print(elem.round(4))
select_1 = bandit_oracle(x, coef_)
select_2 = bandit_low(x, e, coef_)
select_3 = bandit_high(x, e, coef_)
select_4 = bandit_bylearning(x, e, coef_)
#select_5 = bandit_low(x, e, coef_) These algorithm possess some randomness
#random
print(risk_calculator(x, e, coef_, select_1))
print(risk_calculator(x, e, coef_, select_2[0]), 'low')
print(risk_calculator(x, e, coef_, select_3[0]), 'high')
print(risk_calculator(x, e, coef_, select_4[0]), 'bylearning')
select_random = np.random.randint(0, coef_.shape[0], n)
print(risk_calculator(x, e, coef_, select_random), 'random')
select_random = np.random.randint(0, coef_.shape[0], n)
print(risk_calculator(x, e, coef_, select_random), 'random')
#print(risk_calculator(x, e, coef_, select_5[0]))
#print(select_2[1].round(4))
#print(select_4[0])
#print(select_2[0], 'low')
#print(select_3[0], 'high')
for elem in select_3[1]:
pass #print(elem.round(4))
for elem in select_4[1]:
for _ in elem:
pass #print(_.round(4))