论文标题
无需交叉验证：正规化混合企业问题的分析框架（扩展版）
No Cross-Validation Required: An Analytical Framework for Regularized Mixed-Integer Problems (Extended Version)
论文作者
论文摘要
本文开发了一种在一般混合企业问题（MIP）中获得正则系数的最佳值的方法。这种方法消除了在现有的惩罚技术中执行的交叉验证，以获得正则化系数的适当值。我们通过提出一种交替解决MIP的方法来获得此目标。首先，通过正规化，我们将MIP转换为更具数学上的典型形式。然后，我们开发一种迭代算法，以更新解决方案以及正则化（惩罚）系数。我们表明，我们的更新过程保证了算法的收敛性。此外，假设目标函数是连续的，我们得出了收敛速率，正规化系数值的下限以及收敛所需的迭代次数的上限。我们在异质网络中使用无线电访问技术（RAT）选择问题来基准我们方法的性能。仿真结果表明，解决方案的溶液几乎是优先的，并且收敛行为的一致性具有所获得的理论界限。
This paper develops a method to obtain the optimal value for the regularization coefficient in a general mixed-integer problem (MIP). This approach eliminates the cross-validation performed in the existing penalty techniques to obtain a proper value for the regularization coefficient. We obtain this goal by proposing an alternating method to solve MIPs. First, via regularization, we convert the MIP into a more mathematically tractable form. Then, we develop an iterative algorithm to update the solution along with the regularization (penalty) coefficient. We show that our update procedure guarantees the convergence of the algorithm. Moreover, assuming the objective function is continuously differentiable, we derive the convergence rate, a lower bound on the value of regularization coefficient, and an upper bound on the number of iterations required for the convergence. We use a radio access technology (RAT) selection problem in a heterogeneous network to benchmark the performance of our method. Simulation results demonstrate near-optimality of the solution and consistency of the convergence behavior with obtained theoretical bounds.
