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

Zichun Wang, Gar Goei Loke, Ruiting Zuo

TL;DR

The paper tackles decision making under autocorrelated uncertainty by extending Optimize-via-Estimate (OVE) to VARMA processes, producing Autocorrelated-OVE (A-OVE). It derives a Fisher–Neyman decomposition for VARMA to obtain a closed-form, sufficient-statistics–driven optimizer and applies it to a portfolio problem with trading costs. Across synthetic and real data, A-OVE consistently achieves lower out-of-sample regret than standard predict-then-optimize and estimate-then-optimize machine-learning baselines, and shows robustness to mild mis-specification. The work highlights the importance of aligning learning objectives with downstream optimization and points to future extensions, including contextual OVE and nonparametric approaches, for broader impact in data-driven decision problems.

Abstract

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.

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

TL;DR

The paper tackles decision making under autocorrelated uncertainty by extending Optimize-via-Estimate (OVE) to VARMA processes, producing Autocorrelated-OVE (A-OVE). It derives a Fisher–Neyman decomposition for VARMA to obtain a closed-form, sufficient-statistics–driven optimizer and applies it to a portfolio problem with trading costs. Across synthetic and real data, A-OVE consistently achieves lower out-of-sample regret than standard predict-then-optimize and estimate-then-optimize machine-learning baselines, and shows robustness to mild mis-specification. The work highlights the importance of aligning learning objectives with downstream optimization and points to future extensions, including contextual OVE and nonparametric approaches, for broader impact in data-driven decision problems.

Abstract

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.
Paper Structure (22 sections, 7 theorems, 73 equations, 4 figures, 5 tables, 9 algorithms)

This paper contains 22 sections, 7 theorems, 73 equations, 4 figures, 5 tables, 9 algorithms.

Table of Contents

  1. Introduction
  2. Data-Driven Optimization
  3. Contributions and Findings
  4. Preliminaries and Notations
  5. Data-Driven Optimization Paradigms
  6. Problem Formulation under Vector Autoregressive Moving Average Process
  7. Notation
  8. Model and Theory
  9. Sufficient Statistics for $\mathrm{VARMA}$
  10. Portfolio Optimization with Trading Cost
  11. Numerical Experiments
  12. Numerical Results on Synthetic Data
  13. Numerical Results on Real-World Data
  14. Conclusion and Broader Impact
  15. Supplementary Material: Deferred Proofs
  16. ...and 7 more sections

Key Result

Theorem 2.3

[LokeZhuZuo2023] Let $\hat{\bm \xi} \in \hat{\Xi} \subseteq \mathbb{R}^r$ be any sufficient statistic for $\bm \xi$ with Fisher-Neyman factorization $L(\bm Y; \bm \xi) = g_0(\bm Y) g_1(\hat{\bm \xi}(\bm Y), \bm \xi)$ for non-negative $g_0$ and $g_1$. Let $\mathcal{X}(\hat{\bm \xi})$ be the set of fe Under Assumption asmp:convex_C, if there is a re-parameterization $\mathcal{Y}^K \ni \bm Y \mapsto

Figures (4)

  • Figure 1: Relative regret under well-specified setting.
  • Figure 2: Relative regret v.s. MSE under well-specified setting.
  • Figure 3: Relative regret under mis-specified setting.
  • Figure 4: Evaluation on Real-World Data.

Theorems & Definitions (7)

  • Theorem 2.3
  • Theorem 3.2: Fisher-Neyman Decomposition for general $\mathrm{VARMA}(p,q)$
  • Corollary 3.3
  • Lemma A.1
  • Lemma A.2: The Innovation Algorithm of $\{\bm{W}_t\}$
  • Lemma E.1
  • Proposition E.2