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

• URL: http://arxiv.org/abs/2512.06270v1
• Date: Sat, 06 Dec 2025 03:47:29 GMT
• Title: Contextual Strongly Convex Simulation Optimization: Optimize then Predict with Inexact Solutions
• Authors: Nifei Lin, Heng Luo, L. Jeff Hong,
• Abstract summary: We study strongly convex simulation optimization and adopt an "optimize then predict" (OTP) approach for real-time decision making.<n>The central theoretical challenge is to understand how the inexactness of solutions generated by simulation-optimization algorithms affects the optimality gap.
• Score: 0.9303501974597549
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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 $Γ$ between the number of design covariates and the per-covariate simulation effort, and demonstrate the convergence rate can approximately achieve $Γ^{-1}$ 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.

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