# Integrated Conditional Estimation-Optimization

arXiv: https://arxiv.org/abs/2110.12351 · HTML: https://mlsanity.com/paper/2110.12351/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 89 references that are in the map.
- First posted on arXiv 24 Oct 2021.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [MIPaaL: Mixed Integer Program as a Layer](https://mlsanity.com/paper/1907.05912/) (2019)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Learning with Differentiable Perturbed Optimizers](https://mlsanity.com/paper/2002.08676/) (2020)
- [Generalization Bounds in the Predict-then-Optimize Framework](https://mlsanity.com/paper/1905.11488/) (2019)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [End to end learning and optimization on graphs](https://mlsanity.com/paper/1905.13732/) (2019)
- [Fast Rates for Contextual Linear Optimization](https://mlsanity.com/paper/2011.03030/) (2020)
- [From Data to Decisions: Distributionally Robust Optimization is Optimal](https://mlsanity.com/paper/1704.04118/) (2017)
- [Risk Bounds and Calibration for a Smart Predict-then-Optimize Method](https://mlsanity.com/paper/2108.08887/) (2021)
- [Robust Sample Average Approximation](https://mlsanity.com/paper/1408.4445/) (2014)
- [Residuals-based distributionally robust optimization with covariate information](https://mlsanity.com/paper/2012.01088/) (2020)
- [Stochastic Optimization Forests](https://mlsanity.com/paper/2008.07473/) (2020)
- [Risk Guarantees for End-to-End Prediction and Optimization Processes](https://mlsanity.com/paper/2012.15046/) (2020)
- [Data-Pooling in Stochastic Optimization](https://mlsanity.com/paper/1906.00255/) (2019)
- [On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach](https://mlsanity.com/paper/2110.04855/) (2021)
- [Exploiting Problem Structure in Optimization under Uncertainty via Online Convex Optimization](https://mlsanity.com/paper/1709.02490/) (2017)
- [Debiasing In-Sample Policy Performance for Small-Data, Large-Scale Optimization](https://mlsanity.com/paper/2107.12438/) (2021)

## Built on by (most cited first, 25 of 25)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (2023)
- [Decision-Focused Learning with Directional Gradients](https://mlsanity.com/paper/2402.03256/) (2024)
- [Data-Driven Sample Average Approximation with Covariate Information](https://mlsanity.com/paper/2207.13554/) (2022)
- [Contextual Stochastic Bilevel Optimization](https://mlsanity.com/paper/2310.18535/) (2023)
- [Utility-Directed Conformal Prediction: A Decision-Aware Framework for Actionable Uncertainty Quantification](https://mlsanity.com/paper/2410.01767/) (2024)
- [Dissecting the Impact of Model Misspecification in Data-driven Optimization](https://mlsanity.com/paper/2503.00626/) (2025)
- [Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls](https://mlsanity.com/paper/2406.02426/) (2024)
- [Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problems](https://mlsanity.com/paper/2407.17200/) (2024)
- [The Bias-Variance Tradeoff in Data-Driven Optimization: A Local Misspecification Perspective](https://mlsanity.com/paper/2510.18215/) (2025)
- [Decision-Focused Bias Correction for Fluid Approximation](https://mlsanity.com/paper/2512.15726/) (2025)
- [Forecasting Outside the Box: Application-Driven Optimal Pointwise Forecasts for Stochastic Optimization](https://mlsanity.com/paper/2411.03520/) (2024)
- [Sufficient Decision Proxies for Decision-Focused Learning](https://mlsanity.com/paper/2505.03953/) (2025)
- [Gradient boosting for convex cone predict and optimize problems](https://mlsanity.com/paper/2204.06895/) (2022)
- [Decision-Focused Federated Learning Under Heterogeneous Objectives and Constraints](https://mlsanity.com/paper/2604.20031/) (2026)
- [Contextual Scenario Generation for Two-Stage Stochastic Programming](https://mlsanity.com/paper/2502.05349/) (2025)
- ["Over-optimizing" for Normality: Budget-constrained Uncertainty Quantification for Contextual Decision-making](https://mlsanity.com/paper/2503.12747/) (2025)
- [Toward Decision-Oriented Prognostics: An Integrated Estimate-Optimize Framework for Predictive Maintenance](https://mlsanity.com/paper/2506.19698/) (2025)
- [Prescribe-then-Select: Adaptive Policy Selection for Contextual Stochastic Optimization](https://mlsanity.com/paper/2509.08194/) (2025)
- [Simultaneous Learning and Optimization via Misspecified Saddle Point Problems](https://mlsanity.com/paper/2510.05241/) (2025)
- [Autocorrelated Optimize-via-Estimate: Predict-then-Optimize versus Finite-sample Optimal](https://mlsanity.com/paper/2602.01877/) (2026)
- [Convergence Rate of a Functional Learning Method for Contextual Stochastic Optimization](https://mlsanity.com/paper/2603.13048/) (2026)
- [Learning Optimization Proxies for Sequential Contextual Stochastic Programs: An Order Fulfillment Application](https://mlsanity.com/paper/2606.25362/) (2026)
- [Decision-Driven Regularization: A Blended Model for Learning and Optimization](https://mlsanity.com/paper/2608.15124/) (2026)
- [Variable Selection for Feature-Based Newsvendor](https://mlsanity.com/paper/2609.01544/) (2026)

## Abstract (arXiv)

Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of uncertain parameters and then optimizing the objective based on the estimation, we propose an integrated conditional estimation-optimization (ICEO) framework that estimates the underlying conditional distribution of the random parameter while considering the structure of the optimization problem. We directly model the relationship between the conditional distribution of the random parameter and the contextual features, and then estimate the probabilistic model with an objective that aligns with the downstream optimization problem. We show that our ICEO approach is asymptotically consistent under moderate regularity conditions and further provide finite performance guarantees in the form of generalization bounds. Computationally, performing estimation with the ICEO approach is a non-convex and often non-differentiable optimization problem. We propose a general methodology for approximating the potentially non-differentiable mapping from estimated conditional distribution to the optimal decision by a differentiable function, which greatly improves the performance of gradient-based algorithms applied to the non-convex problem. We also provide a polynomial optimization solution approach in the semi-algebraic case. Numerical experiments are also conducted to show the empirical success of our approach in different situations including with limited data samples and model mismatches.