Models that directly optimize for out-of-sample performance in the finite-sample regime have emerged as a promising alternative to traditional estimate-then-optimize approaches in data-driven optimization. In this work, we compare their performance in the context of autocorrelated uncertainties, specifically, under a Vector Autoregressive Moving Average VARMA(p,q) process. We propose an autocorrelated Optimize-via-Estimate (A-OVE) model that obtains an out-of-sample optimal solution as a function of sufficient statistics, and propose a recursive form for computing its sufficient statistics. We evaluate these models on a portfolio optimization problem with trading costs. A-OVE achieves low regret relative to a perfect information oracle, outperforming predict-then-optimize machine learning benchmarks. Notably, machine learning models with higher accuracy can have poorer decision quality, echoing the growing literature in data-driven optimization. Performance is retained under small mis-specification.

翻译：在数据驱动的优化领域，直接针对有限样本情形下的样本外性能进行优化的模型，已成为传统估计-然后-优化方法的一种有前景的替代方案。本文在自相关不确定性的背景下，具体而言是在向量自回归移动平均VARMA(p,q)过程的框架下，比较了这两种方法的性能。我们提出了一种自相关优化-通过-估计模型，该模型能够获得作为充分统计量函数的样本外最优解，并提出了计算其充分统计量的递归形式。我们在考虑交易成本的组合优化问题上对这些模型进行了评估。相较于完美信息预言机，自相关优化-通过-估计模型实现了较低的遗憾值，其表现优于预测-然后-优化的机器学习基准模型。值得注意的是，预测精度更高的机器学习模型可能具有更差的决策质量，这与数据驱动优化领域日益增多的文献观点相呼应。在模型存在轻微设定误差的情况下，其性能依然得以保持。