# Decision-focused Sparse Tangent Portfolio Optimization

arXiv: https://arxiv.org/abs/2607.00581 · HTML: https://mlsanity.com/paper/2607.00581/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 31 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 5 of 5)

- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [A Globally Optimal Portfolio for m-Sparse Sharpe Ratio Maximization](https://mlsanity.com/paper/2410.21100/) (2024)
- [Sparse Portfolio Selection via Quasi-Norm Regularization](https://mlsanity.com/paper/1312.6350/) (2013)
- [Prediction Loss Guided Decision-Focused Learning](https://mlsanity.com/paper/2509.08359/) (2025)

## Built on by (most cited first, 1 of 1)

- [Jacobian Rank Collapse in Decision-Focused Learning](https://mlsanity.com/paper/2609.39261/) (2026)

## Abstract (arXiv)

Sparse tangent portfolio optimization aims to learn an interpretable, low-cardinality portfolio in the tangency direction of the mean-variance frontier. However, the associated cardinality-constrained formulation is NP-hard, and standard predict-then-optimize pipelines often misalign forecasting accuracy with downstream portfolio quality. We propose an end-to-end decision-focused learning framework that reformulates Sharpe ratio maximization as a Disciplined Parametrized Programming (DPP)-compliant convex programming layer and replaces discrete selection with a smooth top-k operator enforcing an exact cardinality k. This enables gradient flow through prediction, asset selection, and re-optimization, allowing the predictive model to directly optimize portfolio performance. Across four major equity markets, our method achieves competitive and often superior out-of-sample Sharpe ratios compared with historical and prediction-focused baselines, with particularly strong gains in larger asset universes. Our hrefhttps://github.com/feuerwerksh/Diffble-card-SRcode is publicly available.