Working with Pulp in python: variables stalled

Question

I'm trying to implement the following LP in Python/Pulp in order to compare to Sklearn:

LP for Support Vector Machine

    #universe
    from pulp import *
    import numpy as np
    from sklearn.metrics.pairwise import rbf_kernel

    #define the function to regresse
    N = 100
    x = np.linspace(0, 2 * np.pi, N)
    y = np.sin(x) + np.random.random(N) * 1
    x.resize(N, 1)
    K = rbf_kernel(x, gamma=5)

    # define de problem for Pulp

    # define the hyper parameters
    C = 10
    eps = 0.1

    # define the variables
    RANGE = list(range(N))
    alpha = pulp.LpVariable.dicts("alpha", (RANGE,), cat='Continuous')
    b = pulp.LpVariable("b", cat='Continuous')
    a = pulp.LpVariable.dicts("a", (RANGE,), lowBound=0, cat='Continuous')
    Eta = pulp.LpVariable.dicts("Eta", (RANGE,), lowBound=0, cat='Continuous')

    prob = LpProblem("Constrained SVM", LpMinimize)

    # implementing the constrains to Pulp
    for i in range(N):
        prob += lpDot(alpha, K[i]) + b - y[i] >= -Eta[i]
        prob += lpDot(alpha, K[i]) + b - y[i] <= Eta[i]
        prob += eps >= 0 #useless constraint
        prob += eps <= Eta[i]
        prob += alpha[i] <= a[i]
        prob += alpha[i] >= -a[i]

    # call the objective function
    prob += lpSum(a) + C * lpSum(Eta)

    #output file
    prob.writeLP("MySVM.lp")

    #launch solver and read result
    prob.solve()
    print("Status:", LpStatus[prob.status])

my issue is the solver doesn't to do anything for alpha and a . They are equal to zero at the end. Is it due to coding error or my LP is badly set?

Answer 1

import numpy as np import matplotlib.pyplot as plt

from sklearn.svm import SVR from sklearn.metrics.pairwise import rbf_kernel from pulp import *

def CompPulpSlk():

N = 100
x = np.linspace(0, 2 * np.pi, N)
y = np.sin(x) + np.random.random(N) * 1

x.resize(N, 1)
K = rbf_kernel(x, gamma=5)

# perform SVR
svr_rbf = SVR(kernel='rbf', C=1e3, gamma=2)
y_rbf = svr_rbf.fit(x, y).predict(x)

# define de problem for Pulp

# define the hyper parameters
C = 10
eps = 0.1

# define the variables
Alpha = pulp.LpVariable.matrix("alpha", list(range(N)), lowBound=-1000, upBound=1000, cat='Continuous')
b = pulp.LpVariable("b", cat='Continuous')
a = pulp.LpVariable.matrix("a", list(range(N)), lowBound=0, cat='Continuous')
Eta = pulp.LpVariable.matrix("Eta", list(range(N)), lowBound=0, cat='Continuous')

prob = LpProblem("Constrained SVM", LpMinimize)

# implementing the constrains to Pulp
for i in range(N):

    prob += lpDot(K[i], Alpha) + b - y[i] >= -Eta[i]
    prob += lpDot(K[i], Alpha) + b - y[i] <= Eta[i]
    prob += eps >= 0
    prob += eps <= Eta[i]
    prob += Alpha[i] <= a[i]
    prob += Alpha[i] >= -a[i]

# call the objective function
prob += lpSum(a[i] for i in range(N)) + C * lpSum(Eta[i] for i in range(N))

#LpSolverDefault.msg = 1
prob.writeLP("MySVM.lp")
prob.solve()

print("Status:", LpStatus[prob.status])

alp = np.zeros(N)
for v in prob.variables():
    if v.name == 'b':
        b = v.varValue
    elif v.name[:5] == 'alpha':
        alp[int(v.name[6:])] = v.varValue

#clean up PULP variables
Alpha.clear()
Eta.clear()
a.clear()

#Projection of the solution from Pulp and Sci-learn
y_pulp = np.zeros(N)
for i in range(N):
    y_pulp[i] = np.dot(alp, K[i, :]) + b

#display result
lw = 2
plt.scatter(x, y, color='darkorange', label='data')
plt.hold('on')
plt.plot(x, y_rbf, color='navy', lw=lw, label='SciLearn')
plt.plot(x, y_pulp, color='cornflowerblue', lw=lw, label='Pulp')
plt.xlabel('data')
plt.ylabel('target')
plt.title('Support Vector Regression')
plt.legend()
plt.show()

CompPulpSlk()