  This paper tackles the problem of minimizing the prediction loss of the
optimal solution (PLS) of the MILP with given data, which is one of the inverse
optimization problems. While existing methods can approximately solve this
problem, their implementation in the high-dimensional case to minimize the PLS
is computationally expensive because they are inefficient in reducing the
prediction loss of weights (PLW). We propose a fast algorithm for minimizing
the PLS of MILP. To demonstrate this property, we attribute the problem of
minimizing the PLS to that of minimizing the suboptimality loss (SL), which is
convex. If the PLS does not vanish, we can adapt the SL to have the estimated
loss (SPO loss) with a positive lower bound, which enables us to evaluate the
PLW. Consequently, we prove that the proposed algorithm can effectively reduce
the PLW and achieve the minimum value of PLS. Our numerical experiments
demonstrated that our algorithm successfully achieved the minimum PLS. Compared
to existing methods, our algorithm exhibited a smaller dimensionality effect
and minimized the PLS in less than 1/7 the number of iterations. Especially in
high dimensions, our algorithm significantly improved the PLS by more than two
orders of magnitude compared to existing algorithms.
