# Generating Input Distributions for Explaining Portfolio Optimization Pipelines

arXiv: https://arxiv.org/abs/2606.25808 · HTML: https://mlsanity.com/paper/2606.25808/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 24 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [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)
- [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)
- [Interpreting Blackbox Models via Model Extraction](https://mlsanity.com/paper/1705.08504/) (2017)
- [Deep Learning in Asset Pricing](https://mlsanity.com/paper/1904.00745/) (2019)
- [Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances](https://mlsanity.com/paper/1802.04885/) (2018)
- [Risk Guarantees for End-to-End Prediction and Optimization Processes](https://mlsanity.com/paper/2012.15046/) (2020)
- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- [Distributionally Robust End-to-End Portfolio Construction](https://mlsanity.com/paper/2206.05134/) (2022)
- [Decision-informed Neural Networks with Large Language Model Integration for Portfolio Optimization](https://mlsanity.com/paper/2502.00828/) (2025)
- [Fast parallel sampling under isoperimetry](https://mlsanity.com/paper/2401.09016/) (2024)
- [Markowitz Portfolio Construction at Seventy](https://mlsanity.com/paper/2401.05080/) (2024)
- [Return Prediction for Mean-Variance Portfolio Selection: How Decision-Focused Learning Shapes Forecasting Models](https://mlsanity.com/paper/2409.09684/) (2024)
- [Decision by Supervised Learning with Deep Ensembles: A Practical Framework for Robust Portfolio Optimization](https://mlsanity.com/paper/2503.13544/) (2025)

## Abstract (arXiv)

We propose a predict-optimize-explain framework that uses gradient-based sample generation to interpret various portfolio models by identifying macroeconomic conditions that induce specified portfolio outcomes. Unlike traditional feature-importance methods, this approach directly probes decision pipelines (predictive models coupled with portfolio optimization) by constructing economically meaningful what-if questions. We focus on four such questions: under what macroeconomic conditions a predict-then-optimize pipeline closes or reverses its return gap with a predict-and-optimize pipeline; what conditions lead a pipeline to diversify rather than concentrate its allocation; when a pipeline trained on calm markets overtakes one trained through crises; and what conditions would let a pipeline match a benchmark return. These examples illustrate how our framework uncovers key behavioral differences between various decision pipelines. Beyond these cases, the proposed framework is flexible and can support a wide range of probing questions tailored to specific portfolio objectives. Our findings highlight the value of integrating prediction, optimization, and explanation to produce more robust and transparent portfolio strategies.