def dfp(inv_H, delta_w, delta_grad, epsilon=1e-7):
"""
DFP is a method very similar to BFGS. It's rank 2 formula update.
It can suffer from round-off error and inaccurate line searches.
"""
inv_H_dot_grad = dot(inv_H, delta_grad)
x = safe_division(outer(delta_w, delta_w), dot(delta_grad, delta_w),
epsilon)
y = safe_division(tf.matmul(outer(inv_H_dot_grad, delta_grad), inv_H),
dot(delta_grad, inv_H_dot_grad), epsilon)
return inv_H - y + x
def bfgs(inv_H, delta_w, delta_grad, epsilon=1e-7):
"""
It can suffer from round-off error and inaccurate line searches.
"""
n_parameters = int(inv_H.shape[0])
I = tf.eye(n_parameters)
rho = safe_reciprocal(dot(delta_grad, delta_w), epsilon)
X = I - outer(delta_w, delta_grad) * rho
X_T = tf.transpose(X)
Z = rho * outer(delta_w, delta_w)
return tf.matmul(X, tf.matmul(inv_H, X_T)) + Z
def sr1(inv_H, delta_w, delta_grad, epsilon=1e-7):
"""
Symmetric rank 1 (SR1). Generates update for the inverse hessian
matrix adding symmetric rank-1 matrix. It's possible that there is no
rank 1 updates for the matrix and in this case update won't be applied
and original inverse hessian will be returned.
"""
param = delta_w - dot(inv_H, delta_grad)
denominator = dot(param, delta_grad)
return tf.where(
# This check protects from the cases when update
# doesn't exist. It's possible that during certain
# iteration there is no rank-1 update for the matrix.
tf.less(tf.abs(denominator),
epsilon * tf.norm(param) * tf.norm(delta_grad)),
inv_H,
inv_H + outer(param, param) / denominator)
