# Estimating Covariance for Global Minimum Variance Portfolio: A Decision-Focused Learning Approach

arXiv: https://arxiv.org/abs/2508.10776 · HTML: https://mlsanity.com/paper/2508.10776/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 14 Aug 2025.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [Distributionally Robust End-to-End Portfolio Construction](https://mlsanity.com/paper/2206.05134/) (2022)
- [Decision-Aware Learning for Optimizing Health Supply Chains](https://mlsanity.com/paper/2211.08507/) (2022)
- [Non-linear shrinkage of the price return covariance matrix is far from optimal for portfolio optimisation](https://mlsanity.com/paper/2112.07521/) (2021)
- [Port Selection for Fluid Antenna Systems](https://mlsanity.com/paper/2201.05702/) (2022)

## Built on by (most cited first, 3 of 3)

- [The Decision Geometry of Covariance Estimation for the Global Minimum-Variance Portfolio under Heavy Tails](https://mlsanity.com/paper/2606.27462/) (2026)
- [Physics-Informed Singular-Value Learning for Cross-Covariances Forecasting in Financial Markets](https://mlsanity.com/paper/2601.07687/) (2026)
- [Jacobian Rank Collapse in Decision-Focused Learning](https://mlsanity.com/paper/2609.39261/) (2026)

## Abstract (arXiv)

Portfolio optimization constitutes a cornerstone of risk management by quantifying the risk-return trade-off. Since it inherently depends on accurate parameter estimation under conditions of future uncertainty, the selection of appropriate input parameters is critical for effective portfolio construction. However, most conventional statistical estimators and machine learning algorithms determine these parameters by minimizing mean-squared error (MSE), a criterion that can yield suboptimal investment decisions. In this paper, we adopt decision-focused learning (DFL) - an approach that directly optimizes decision quality rather than prediction error such as MSE - to derive the global minimum-variance portfolio (GMVP). Specifically, we theoretically derive the gradient of decision loss using the analytic solution of GMVP and its properties regarding the principal components of itself. Through extensive empirical evaluation, we show that prediction-focused estimation methods may fail to produce optimal allocations in practice, whereas DFL-based methods consistently deliver superior decision performance. Furthermore, we provide a comprehensive analysis of DFL's mechanism in GMVP construction, focusing on its volatility reduction capability, decision-driving features, and estimation characteristics.