We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to an $\epsilon$-optimal solution with high probability. Numerical experiments on several problems show that stochastic cutting planes is able to deliver a multiple order-of-magnitude speedup compared to the standard cutting-plane method. We further experimentally explore the lower limits of sampling for stochastic cutting planes and show that for many problems, a sampling size of $O(\sqrt[3]{n})$ appears to be sufficient for high quality solutions.

翻译：我们为大量数据驱动的非线性混合集成优化(MINLO)问题引入了切除机法的随机版本。 我们发现,在非常薄弱的假设下,切除机算算法能够以极有可能的极好方法趋同到$\ epsilon$-最优的解决方案。 对几个问题的数值实验表明,切除机能够提供与标准切除机法相比的多重测序速度。 我们进一步实验探索对切除机取样的下限,并表明对于许多问题来说,以$O(sqrt[3]{n}]$(sqrt[3]{n}]$(美元)的取样规模似乎足以满足高质量的解决方案。