Autocorrelated Optimize-via-Estimate: Predict-then-Optimize versus Finite-sample Optimal

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.