# "Over-optimizing" for Normality: Budget-constrained Uncertainty Quantification for Contextual Decision-making

arXiv: https://arxiv.org/abs/2503.12747 · HTML: https://mlsanity.com/paper/2503.12747/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## Builds on (most cited first, 11 of 11)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [A System for Massively Parallel Hyperparameter Tuning](https://mlsanity.com/paper/1810.05934/) (2018)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Using Wasserstein Generative Adversarial Networks for the Design of Monte Carlo Simulations](https://mlsanity.com/paper/1909.02210/) (2019)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [Risk Guarantees for End-to-End Prediction and Optimization Processes](https://mlsanity.com/paper/2012.15046/) (2020)
- [Dynamic optimization with side information](https://mlsanity.com/paper/1907.07307/) (2019)
- [Data-Driven Sample Average Approximation with Covariate Information](https://mlsanity.com/paper/2207.13554/) (2022)
- [On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach](https://mlsanity.com/paper/2110.04855/) (2021)
- [A Conformal Approach to Feature-based Newsvendor under Model Misspecification](https://mlsanity.com/paper/2412.13159/) (2024)

## Abstract (arXiv)

We study uncertainty quantification for contextual stochastic optimization, focusing on weighted sample average approximation (wSAA), which uses machine-learned relevance weights based on covariates. Although wSAA is widely used for contextual decisions, its uncertainty quantification remains limited. In addition, computational budgets tie sample size to optimization accuracy, creating a coupling that standard analyses often ignore. We establish central limit theorems for wSAA and construct asymptotic-normality-based confidence intervals for optimal conditional expected costs. We analyze the statistical--computational tradeoff under a computational budget, characterizing how to allocate resources between sample size and optimization iterations to balance statistical and optimization errors. These allocation rules depend on structural parameters of the objective; misspecifying them can break the asymptotic optimality of the wSAA estimator. We show that ``over-optimizing'' (running more iterations than the nominal rule) mitigates this misspecification and preserves asymptotic normality, at the expense of a slight slowdown in the convergence rate of the budget-constrained estimator. The common intuition that ``more data is better'' can fail under computational constraints: increasing the sample size may worsen statistical inference by forcing fewer algorithm iterations and larger optimization error. Our framework provides a principled way to quantify uncertainty for contextual decision-making under computational constraints. It offers practical guidance on allocating limited resources between data acquisition and optimization effort, clarifying when to prioritize additional optimization iterations over more data to ensure valid confidence intervals for conditional performance.