Specific Iteration Complexity of Actual Information-Pushed Inverse Optimization for Integer Linear Packages

arXiv:2607.22263v1 Announce Sort: cross
Summary: A knowledge-driven inverse optimization drawback (DDIOP) is the issue of estimating the objective-function parameters (weights) that designate noticed optimal-solution knowledge, and it arises in lots of purposes, together with integer linear programming (ILP). It’s identified that, by making use of gradient-based optimization strategies to the suboptimality loss, the inverse optimization of ILPs will be solved precisely inside finitely many oracle iterations, and that the required variety of iterations is bounded as $T=O(1/gamma(ell_{mathrm{sub}})^2)$ by way of a problem-dependent geometric fixed $gamma(ell_{mathrm{sub}})$. Nonetheless, no technique of bounding $gamma(ell_{mathrm{sub}})$ from beneath as a operate of the issue dimension has been out there, and therefore the variety of iterations couldn’t be given as an specific operate of the issue dimension. We subsequently give, when the ahead drawback is an integer linear program (ILP), the variety of iterations ample for projected subgradient descent utilized to the suboptimality loss to attain precise consistency with the noticed knowledge, as a completely specific operate of the variety of samples, the dimension of the options, the ranges of the options, and the construction of the constraint coefficient matrix, as much as polynomial elements within the primary constants (the diameter of the load set, the step-size parameter, and the Lipschitz fixed of the suboptimality loss).



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