# Distributionally Robust End-to-End Portfolio Construction

arXiv: https://arxiv.org/abs/2206.05134 · HTML: https://mlsanity.com/paper/2206.05134/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 63 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [Generative Adversarial Networks for Financial Trading Strategies Fine-Tuning and Combination](https://mlsanity.com/paper/1901.01751/) (2019)
- [Residuals-based distributionally robust optimization with covariate information](https://mlsanity.com/paper/2012.01088/) (2020)
- [Task-based End-to-end Model Learning in Stochastic Optimization](https://mlsanity.com/paper/1703.04529/) (2017)
- [Data-driven distributionally robust risk parity portfolio optimization](https://mlsanity.com/paper/2110.06464/) (2021)

## Built on by (most cited first, 17 of 17)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [Decision-informed Neural Networks with Large Language Model Integration for Portfolio Optimization](https://mlsanity.com/paper/2502.00828/) (2025)
- [Differentiable Distributionally Robust Optimization Layers](https://mlsanity.com/paper/2406.16571/) (2024)
- [Return Prediction for Mean-Variance Portfolio Selection: How Decision-Focused Learning Shapes Forecasting Models](https://mlsanity.com/paper/2409.09684/) (2024)
- [End-to-End Large Portfolio Optimization for Variance Minimization with Neural Networks through Covariance Cleaning](https://mlsanity.com/paper/2507.01918/) (2025)
- [Decision-Focused Learning via Tangent-Space Projection of Prediction Error](https://mlsanity.com/paper/2605.01361/) (2026)
- [Estimating Covariance for Global Minimum Variance Portfolio: A Decision-Focused Learning Approach](https://mlsanity.com/paper/2508.10776/) (2025)
- [Robust Generalization with Adaptive Optimal Transport Priors for Decision-Focused Learning](https://mlsanity.com/paper/2602.01427/) (2026)
- [Temporal Representation Learning for Stock Similarities and Its Applications in Investment Management](https://mlsanity.com/paper/2407.13751/) (2024)
- [LambdaRankIC: Directly Optimizing Rank IC for Financial Prediction](https://mlsanity.com/paper/2605.00501/) (2026)
- [The Decision Geometry of Covariance Estimation for the Global Minimum-Variance Portfolio under Heavy Tails](https://mlsanity.com/paper/2606.27462/) (2026)
- [Signature-Informed Transformer for Asset Allocation](https://mlsanity.com/paper/2510.03129/) (2025)
- [Integrated Prediction and Multi-period Portfolio Optimization](https://mlsanity.com/paper/2512.11273/) (2025)
- [Risk-Averse Wasserstein Distributionally Robust Online Learning](https://mlsanity.com/paper/2602.20403/) (2026)
- [Generating Input Distributions for Explaining Portfolio Optimization Pipelines](https://mlsanity.com/paper/2606.25808/) (2026)
- [Generative Distributionally Robust Optimization](https://mlsanity.com/paper/2607.24983/) (2026)

## Abstract (arXiv)

We propose an end-to-end distributionally robust system for portfolio construction that integrates the asset return prediction model with a distributionally robust portfolio optimization model. We also show how to learn the risk-tolerance parameter and the degree of robustness directly from data. End-to-end systems have an advantage in that information can be communicated between the prediction and decision layers during training, allowing the parameters to be trained for the final task rather than solely for predictive performance. However, existing end-to-end systems are not able to quantify and correct for the impact of model risk on the decision layer. Our proposed distributionally robust end-to-end portfolio selection system explicitly accounts for the impact of model risk. The decision layer chooses portfolios by solving a minimax problem where the distribution of the asset returns is assumed to belong to an ambiguity set centered around a nominal distribution. Using convex duality, we recast the minimax problem in a form that allows for efficient training of the end-to-end system.