# Contextual Strongly Convex Simulation Optimization: Optimize then Predict with Inexact Solutions

arXiv: https://arxiv.org/abs/2512.06270 · HTML: https://mlsanity.com/paper/2512.06270/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 27 references that are in the map.
- First posted on arXiv 6 Dec 2025.

## Builds on (most cited first, 9 of 9)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality](https://mlsanity.com/paper/2207.04173/) (2022)
- [Ranking and Selection with Covariates for Personalized Decision Making](https://mlsanity.com/paper/1710.02642/) (2017)
- [Surrogate-Based Simulation Optimization](https://mlsanity.com/paper/2105.03893/) (2021)
- [Quasi-uniform designs with optimal and near-optimal uniformity constant](https://mlsanity.com/paper/2112.10401/) (2021)
- [Review of Large-Scale Simulation Optimization](https://mlsanity.com/paper/2403.15669/) (2024)
- [Regret Optimality of Sample Average Approximation for Data-Driven Newsvendor Problems: A General Optimization Perspective](https://mlsanity.com/paper/2407.04900/) (2024)
- [Convergence Analysis of Stochastic Kriging-Assisted Simulation with Random Covariates](https://mlsanity.com/paper/2211.13685/) (2022)

## Built on by (most cited first, 2 of 2)

- [Reliable Real-Time Value at Risk Estimation via Quantile Regression Forest with Conformal Calibration](https://mlsanity.com/paper/2602.01912/) (2026)
- [Learn-Then-Differentiate Gradient Estimation](https://mlsanity.com/paper/2609.38842/) (2026)

## Abstract (arXiv)

In this work, we study contextual strongly convex simulation optimization and adopt an "optimize then predict" (OTP) approach for real-time decision making. In the offline stage, simulation optimization is conducted across a set of covariates to approximate the optimal-solution function; in the online stage, decisions are obtained by evaluating this approximation at the observed covariate. The central theoretical challenge is to understand how the inexactness of solutions generated by simulation-optimization algorithms affects the optimality gap, which is overlooked in existing studies. To address this, we develop a unified analysis framework that explicitly accounts for both solution bias and variance. Using Polyak-Ruppert averaging SGD as an illustrative simulation-optimization algorithm, we analyze the optimality gap of OTP under four representative smoothing techniques: k nearest neighbor, kernel smoothing, linear regression, and kernel ridge regression. We establish convergence rates, derive the optimal allocation of the computational budget Gamma between the number of design covariates and the per-covariate simulation effort, and demonstrate the convergence rate can approximately achieve Gamma-1 under appropriate smoothing technique and sample-allocation rule. Finally, through a numerical study, we validate the theoretical findings and demonstrate the effectiveness and practical value of the proposed approach.