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oracles.py
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oracles.py
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import numpy as np
class BaseOracle:
"""
Base class for implementation of oracles. (based on https://github.com/arodomanov/cmc-mipt17-opt-course/blob/master/task4/oracles.py)
"""
def __init__(self):
pass
def func(self, x):
"""
Computes the value of function at point x.
:param x: point for computation
:return: function value
"""
raise NotImplementedError('Func oracle is not implemented.')
def grad(self, x):
"""
Computes the grad at point x.
:param x: point for computation
:return: gradient
"""
raise NotImplementedError('Grad oracle is not implemented.')
def grad_stoh(self, x, i):
"""
Computes the grad's component i at point x.
:param x: point for computation
:return: gradient[i]
"""
raise NotImplementedError('Grad stoh oracle is not implemented.')
def metrics(self):
"""
Get metrics
:return: dict with metrics
"""
raise NotImplementedError('Metrics oracle is not implemented.')
class BaseSaddleOracle:
"""
Base class for implementation of saddle oracles.
"""
def __init__(self):
pass
def func(self, x, y):
"""
Computes the value of function at point x, y.
:param x, y: point for computation
:return: function value
"""
raise NotImplementedError('Func oracle is not implemented.')
def grad_x(self, x, y):
"""
Computes the grad by x at point x, y.
:param x, y: point for computation
:return: gradient
"""
raise NotImplementedError('Grad oracle is not implemented.')
def grad_y(self, x, y):
"""
Computes the grad by y at point x, y.
:param x, y: point for computation
:return: gradient
"""
raise NotImplementedError('Grad oracle is not implemented.')
def grad_y_stoh(self, x, y, i):
"""
Computes the grad_y[i] at point x, y.
:param x, y: point for computation
:return: gradient
"""
raise NotImplementedError('Grad oracle is not implemented.')
def grad_x_stoh(self, x, y, i):
"""
Computes the grad_x[i] at point x, y.
:param x, y: point for computation
:return: gradient
"""
raise NotImplementedError('Grad oracle is not implemented.')
def metrics(self):
"""
Get metrics
:return: dict with metrics
"""
raise NotImplementedError('Metrics oracle is not implemented.')
class KOracle(BaseOracle):
def __init__(self, f, k):
self.f = f
self.k = k
def func(self, x):
return self.k * self.f.func(x)
def grad(self, x):
return self.k * self.f.grad(x)
def grad_stoh(self, x, i):
return self.k * self.f.grad_stoh(x, i)
def metrics(self):
return self.f.metrics()
class FixedXOracle(BaseOracle):
"""
Saddle oracle with fixed x coordinate
"""
def __init__(self, saddle, x):
self.saddle = saddle
self.x = x
def func(self, y):
return self.saddle.func(self.x, y)
def grad(self, y):
return self.saddle.grad_y(self.x, y)
def grad_stoh(self, y, i):
return self.saddle.grad_y_stoh(self.x, y, i)
class PowerOracle(BaseOracle):
def __init__(self, p, k):
self.p = p
self.k = k
self.stat = {'f_calls': 0, 'g_calls': 0}
def func(self, x):
self.stat['f_calls'] += 1
return self.k * np.abs(x ** self.p).sum()
def grad(self, x):
self.stat['g_calls'] += 1
return self.k * self.p * (x ** (self.p - 1))
def grad_stoh(self, x, i):
self.stat['g_calls'] += 1
return self.k * self.p * (x[i] ** (self.p - 1))
def metrics(self):
return self.stat
class MultiplyOracle(BaseSaddleOracle):
"""
Used only for tests
"""
def __init__(self, k):
self.k = k
self.stat = {'f_calls': 0, 'g_calls': 0}
def func(self, x, y):
self.stat['f_calls'] += 1
return self.k * np.dot(x, y)
def grad_x(self, x, y):
self.stat['g_calls'] += 1
return self.k * y
def grad_x_stoh(self, x, y, i):
self.stat['g_calls'] += 1
return self.k * y[i]
def grad_y(self, x, y):
self.stat['g_calls'] += 1
return self.k * x
def grad_y_stoh(self, x, y, i):
self.stat['g_calls'] += 1
return self.k * x[i]
def metrics(self):
return self.stat
class ConstantOracle(BaseOracle):
def __init__(self, C):
self.C = C
self.stat = {'f_calls': 0, 'g_calls': 0}
def func(self, x):
self.stat['f_calls'] += 1
return self.C
def grad(self, x):
self.stat['g_calls'] += 1
return 0
def metrics(self):
return self.stat
class SumOracle(BaseOracle):
"""
Oracle for summing provided oracles
"""
def __init__(self, lst):
self.lst = lst
self.stat = {'f_calls': 0, 'g_calls': 0}
def func(self, x):
self.stat['f_calls'] += 1
res = 0
for o in self.lst:
res += o.func(x)
return res
def grad(self, x):
self.stat['g_calls'] += 1
res = 0
for o in self.lst:
res += o.grad(x)
return res
def grad_stoh(self, x, i):
self.stat['g_calls'] += 1
res = 0
for o in self.lst:
res += o.grad_stoh(x)
return res
def metrics(self):
return self.stat
# oracles for experiments
class MultiplySaddleOracle(BaseSaddleOracle):
"""
Oracle for bilinear form
"""
def __init__(self, A):
self.A = np.array(A)
self.stat = {'f_calls': 0, 'g_calls': 0,
'g_calls_x': 0, 'g_calls_y': 0}
def func(self, x, y):
self.stat['f_calls'] += 1
return np.dot(x, np.dot(self.A, y))
def grad_x(self, x, y):
self.stat['g_calls_x'] += 1
return np.dot(self.A, y)
def grad_x_stoh(self, x, y, i):
self.stat['g_calls_x'] += 1
return np.dot(self.A[i], y)
def grad_y(self, x, y):
self.stat['g_calls_y'] += 1
return np.dot(x, self.A)
def grad_y_stoh(self, x, y, i):
self.stat['g_calls_y'] += 1
return np.dot(x, self.A[:, i])
def metrics(self):
self.stat['g_calls'] = self.stat['g_calls_x'] + self.stat['g_calls_y']
return self.stat
class MatrixFromYSaddleOracle(BaseSaddleOracle):
"""
Oracle for function <x, A(y) x>,
where A(y) = \sum_{i= 1}^{k} M_k \cdot a_i,
where a_i = B_i \cdot y
"""
def __init__(self, matrixes, B):
self.matrixes = matrixes
self.B = B
self.stat = {'f_calls': 0, 'g_calls': 0,
'g_calls_x': 0, 'g_calls_y': 0}
def func(self, x, y):
b = np.dot(self.B, y)
A = 0
for i in range(len(self.matrixes)):
A += b[i] * self.matrixes[i]
return np.dot(x.T, np.dot(A, x))
def grad_x(self, x, y):
self.stat['g_calls_x'] += 1
b = np.dot(self.B, y)
A = 0
for j in range(len(self.matrixes)):
A += b[j] * self.matrixes[j]
return np.dot(2 * A, x)
def grad_x_stoh(self, x, y, i):
self.stat['g_calls_x'] += 1
b = np.dot(self.B, y)
A = 0
for j in range(len(self.matrixes)):
A += b[j] * self.matrixes[j][i]
return np.dot(2 * A, x)
def grad_y(self, x, y):
self.stat['g_calls_y'] += 1
res = 0
for j in range(len(self.matrixes)):
res += np.dot(x,
np.dot(self.matrixes[j], x)) * self.B[j] * y
return res
def grad_y_stoh(self, x, y, i):
self.stat['g_calls_y'] += 1
res = 0
for j in range(len(self.matrixes)):
res += np.dot(x, np.dot(self.matrixes[j], x)
) * self.B[j][i] * y[i]
return res
def metrics(self):
self.stat['g_calls'] = self.stat['g_calls_x'] + self.stat['g_calls_y']
return self.stat
class QuadraticFormOracle(BaseOracle):
"""
Oracle for quadratic form
"""
def __init__(self, A):
self.A = np.array(A)
self.stat = {'f_calls': 0, 'g_calls': 0}
def func(self, x):
self.stat['f_calls'] += 1
return np.dot(np.dot(x, self.A), x)
def grad(self, x):
self.stat['g_calls'] += 1
return 2 * np.dot(self.A, x)
def grad_stoh(self, x, i):
self.stat['g_calls'] += 1
return 2 * np.dot(self.A[i], x)
def metrics(self):
return self.stat
class LogSumExpOracle(BaseOracle):
"""
Oracle for function $\log(\sum_{k=1} ^ p \exp \langle A_k, x\rangle)$
"""
def __init__(self, A):
self.A = np.array(A)
self.stat = {'f_calls': 0, 'g_calls': 0}
def func(self, x):
self.stat['f_calls'] += 1
# https://github.com/dmivilensky/composite-accelerated-method/blob/master/meta-algorithm-vs-ms.ipynb
t = np.dot(self.A, x)
u = t.max()
t -= u
return u + np.log(np.sum(np.exp(t)))
def grad(self, x):
self.stat['g_calls'] += 1
# https://github.com/dmivilensky/composite-accelerated-method/blob/master/meta-algorithm-vs-ms.ipynb
s = np.dot(self.A, x)
b = s.max()
z = np.exp(s - b)
return np.dot(self.A.T, z) / np.dot(np.ones(self.A.shape[0]), z)
def grad_stoh(self, x, i):
self.stat['g_calls'] += 1
# https://github.com/dmivilensky/composite-accelerated-method/blob/master/meta-algorithm-vs-ms.ipynb
s = np.dot(self.A, x)
b = s.max()
z = np.exp(s - b)
return np.dot(self.A.T[i], z) / np.dot(np.ones(self.A.shape[0]), z)
def metrics(self):
return self.stat
class NormOracle(BaseOracle):
"""
UNUSED
"""
def __init__(self, G):
self.G = G
self.stat = {'f_calls': 0, 'g_calls': 0}
def func(self, x):
self.stat['f_calls'] += 1
return np.dot(x, np.dot(self.G, x)) / 2
def grad(self, x):
self.stat['g_calls'] += 1
return np.dot(self.G, x)
def grad_stoh(self, x):
self.stat['g_calls'] += 1
return np.dot(self.G[i], x)
def metrics(self):
return self.stat