L-BFGS solver stops working when i increase input array (“Line search cannot locate an adequate point…”)

问题

The Optimization for my Recommender system:

min|| R - XY ||

R: Ratingmatrix

X: UserxFaktor

Y: FaktorxItem

stops working when i increase the size of the input. Just for clarification the code in short:

k = 3
n = 10 #5
m= 50 #10

R=np.array(np.arange(n*m)).reshape(n, m)
Z0 = np.array(np.random.random(n*k+k*m))

def whatineed (Z):
    return np.linalg.norm(R - np.dot(Z[:(n*k)].reshape(n,k),Z[(n*k):].reshape(k,m)))


def VectorizeX(Matrix):
    i, j = Matrix.shape
    return (Matrix.reshape((i * j, 1), order='C'))

def VectorizeY(Matrix):
    i, j = Matrix.shape
    return (Matrix.reshape((i * j, 1), order='C'))



def gradZ(Z):
    Xk = Z[:(n*k)].reshape((n,k), order='C')
    Yk = Z[(n*k):].reshape((k,m), order='C')
    grad_X = -np.dot(R - np.dot(Xk, Yk), Yk.T)
    grad_Y = -np.dot(Xk.T, R - np.dot(Xk, Yk))
    return np.concatenate((VectorizeX(grad_X), VectorizeY(grad_Y)), axis=0)

A = minimize(fun=whatineed, x0=Z0, jac=gradZ, method='L-BFGS-B', options={'disp': 1})

X = A.x[:(n*k)].reshape(n,k)
Y = A.x[(n*k):].reshape(k,m)
print(np.linalg.norm(R - np.dot(X,Y)))

the commented n, m are one example where it still works (GREAT). and then all of the sudden nothing. Below the error message

ABNORMAL_TERMINATION_IN_LNSRCH                              

 Line search cannot locate an adequate point after 20 function
  and gradient evaluations.  Previous x, f and g restored.
 Possible causes: 1 error in function or gradient evaluation;
                  2 rounding error dominate computation.

 Cauchy                time 0.000E+00 seconds.
 Subspace minimization time 0.000E+00 seconds.
 Line search           time 0.000E+00 seconds.

 Total User time 0.000E+00 seconds.

What caused this issue and what is the workaround?

来源：https://stackoverflow.com/questions/54155873/l-bfgs-solver-stops-working-when-i-increase-input-array-line-search-cannot-loc

标签

python

dimensions

recommendation-engine