# Contextual Preference Distribution Learning

arXiv: https://arxiv.org/abs/2603.17139 · HTML: https://mlsanity.com/paper/2603.17139/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 53 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Builds on (most cited first, 28 of 28)

- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Learning with Differentiable Perturbed Optimizers](https://mlsanity.com/paper/2002.08676/) (2020)
- [Contrastive Losses and Solution Caching for Predict-and-Optimize](https://mlsanity.com/paper/2011.05354/) (2020)
- [Inverse Optimization: Theory and Applications](https://mlsanity.com/paper/2109.03920/) (2021)
- [Data-driven Inverse Optimization with Imperfect Information](https://mlsanity.com/paper/1512.05489/) (2015)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Residuals-based distributionally robust optimization with covariate information](https://mlsanity.com/paper/2012.01088/) (2020)
- [Contextual Inverse Optimization: Offline and Online Learning](https://mlsanity.com/paper/2106.14015/) (2021)
- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (2023)
- [Predict-then-Calibrate: A New Perspective of Robust Contextual LP](https://mlsanity.com/paper/2305.15686/) (2023)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [Dynamic optimization with side information](https://mlsanity.com/paper/1907.07307/) (2019)
- [Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming](https://mlsanity.com/paper/2301.11260/) (2023)
- [On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach](https://mlsanity.com/paper/2110.04855/) (2021)
- [Adaptive Perturbation-Based Gradient Estimation for Discrete Latent Variable Models](https://mlsanity.com/paper/2209.04862/) (2022)
- [Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning](https://mlsanity.com/paper/2307.05213/) (2023)
- [A deep inverse reinforcement learning approach to route choice modeling with context-dependent rewards](https://mlsanity.com/paper/2206.10598/) (2022)
- [Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithms](https://mlsanity.com/paper/2305.07730/) (2023)
- [MPAX: Mathematical Programming in JAX](https://mlsanity.com/paper/2412.09734/) (2024)
- [Vehicle routing by learning from historical solutions](https://mlsanity.com/paper/1909.07893/) (2019)
- [Conformal Inverse Optimization](https://mlsanity.com/paper/2402.01489/) (2024)
- [Learning from Stochastically Revealed Preference](https://mlsanity.com/paper/2206.01484/) (2022)
- [Learning Consumer Preferences from Bundle Sales Data](https://mlsanity.com/paper/2209.04942/) (2022)
- [Predictive inference for travel time on transportation networks](https://mlsanity.com/paper/2004.11292/) (2020)

## Abstract (arXiv)

Decision-making problems often feature uncertainty stemming from heterogeneous and context-dependent human preferences. To address this, we propose a sequential learning-and-optimization pipeline to learn preference distributions and leverage them to solve downstream problems, for example risk-averse formulations. We focus on human choice settings that can be formulated as (integer) linear programs. In such settings, existing inverse optimization and choice modelling methods infer preferences from observed choices but typically produce point estimates or fail to capture contextual shifts, making them unsuitable for risk-averse decision-making. Using a bounded-variance score function gradient estimator, we train a predictive model mapping contextual features to a rich class of parameterizable distributions. This approach yields a maximum likelihood estimate. The model generates scenarios for unseen contexts in the subsequent optimization phase. In a synthetic ridesharing environment, our approach reduces average post-decision surprise by up to 114× compared to a risk-neutral approach with perfect predictions and up to 25× compared to leading risk-averse baselines.