identity check for 5 random pairs of policies
  J_new - J_old = -0.105563840069   lemma = -0.105563840069   |diff| = 5.6e-16
  J_new - J_old = -0.311667151668   lemma = -0.311667151668   |diff| = 1.7e-16
  J_new - J_old = +0.203577005002   lemma = +0.203577005002   |diff| = 3.3e-16
  J_new - J_old = -0.068012853634   lemma = -0.068012853634   |diff| = 4.3e-16
  J_new - J_old = +0.166001950734   lemma = +0.166001950734   |diff| = 5.6e-16

surrogate error along the line theta_old + s * direction
     s    alpha  true diff  surrogate    |error|      bound  error/alpha^2
  0.05   0.0478    0.00469    0.00477   7.32e-05   1.60e-01          0.032
   0.1   0.1001    0.00878    0.00908   2.95e-04   7.01e-01          0.029
   0.2   0.2139    0.01571    0.01686   1.16e-03   3.20e+00          0.025
   0.4   0.4367    0.02975    0.03364   3.89e-03   1.34e+01          0.020
   0.8   0.6778    0.07036    0.07900   8.63e-03   3.22e+01          0.019
   1.6   0.7442    0.12336    0.13699   1.36e-02   3.88e+01          0.025
