arXiv subjects

Jianzhong Du

Publications and source records attributed to Jianzhong Du.

4 recordsLinked to original sources

arXiv2026

Understanding the Variance Dichotomy in Continuous Simulation Optimization: A Minimax Lower Bound Perspective

This paper studies the variance dichotomy in continuous simulation optimization (CSO). Existing literature shows a sharp contrast between deterministic CSO and stochastic CSO, with convergence rates in stochastic settings appearing insensitive to the magnitude of the noise variance. However, this asymptotic view does not fully explain the behavior of CSO under finite simulation budgets, especially in low-noise settings. To address this gap, this work develops a minimax lower-bound analysis and shows that the complexity is decided by the maximum of a variance-dependent term and a variance-independent term. When the simulation budget is not very large and the noise variance is low, the variance-independent term dominates, implying that low-noise stochastic CSO has essentially the same complexity as deterministic CSO. As the budget increases, the variance-dependent term becomes dominant, and the convergence behavior of stochastic CSO transitions to a slower regime determined jointly by the noise variance and the simulation budget.

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arXiv2025

Optimal Simulation Budget Allocation Under Unknown Sampling Variance

The ranking and selection problem is a popular framework in the simulation literature for studying optimal information collection. We study a version of this problem in which the simulation output for each design is normally distributed with both its mean and variance being unknown. Using a Bayesian representation of the probability of correct selection, which allows us to explicitly model uncertainty about the variance, we provide a theoretical characterization of the optimal allocation of the simulation budget. Prior work on optimal budget allocation was unable to distinguish between known and unknown sampling variance. We show the impact of this type of uncertainty on the allocation, and design new sequential procedures that can be guaranteed to learn the optimal allocation asymptotically without the need for tuning or forced exploration.

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arXiv2023

A Contextual Ranking and Selection Method for Personalized Medicine

Problem definition: Personalized medicine (PM) seeks the best treatment for each patient among a set of available treatment methods. Since a specific treatment does not work well on all patients, traditionally, the best treatment was selected based on the doctor's personal experience and expertise, which is subject to human errors. In the meantime, stochastic models have been well developed in the literature for a lot of major diseases. This gives rise to a simulation-based solution for PM, which uses the simulation tool to evaluate the performance for pairs of treatment and patient biometric characteristics, and based on that, selects the best treatment for each patient characteristics. Methodology/results: In this research, we extend the ranking and selection (R&S) model in simulation-based decision making to solving PM. The biometric characteristics of a patient is treated as a context for R&S, and we call it contextual ranking and selection (CR&S). We consider two formulations of CR&S with small and large context spaces respectively and develop new techniques for solving them and identifying the rate-optimal budget allocation rules. Based on them, two selection algorithms are proposed, which can be shown to be numerically superior via a set of tests on abstract and real-world examples. Managerial implications: This research provides a systematic way of conducting simulation-based decision-making for PM. To improve the overall decision quality for the possible contexts, more simulation efforts should be devoted to contexts in which it is difficult to distinguish between the best treatment and non-best treatments, and our results quantify the optimal tradeoff of the simulation efforts between the pairs of contexts and treatments.

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arXiv2022

Convergence Analysis of Stochastic Kriging-Assisted Simulation with Random Covariates

We consider performing simulation experiments in the presence of covariates. Here, covariates refer to some input information other than system designs to the simulation model that can also affect the system performance. To make decisions, decision makers need to know the covariate values of the problem. Traditionally in simulation-based decision making, simulation samples are collected after the covariate values are known; in contrast, as a new framework, simulation with covariates starts the simulation before the covariate values are revealed, and collects samples on covariate values that might appear later. Then, when the covariate values are revealed, the collected simulation samples are directly used to predict the desired results. This framework significantly reduces the decision time compared to the traditional way of simulation. In this paper, we follow this framework and suppose there are a finite number of system designs. We adopt the metamodel of stochastic kriging (SK) and use it to predict the system performance of each design and the best design. The goal is to study how fast the prediction errors diminish with the number of covariate points sampled. This is a fundamental problem in simulation with covariates and helps quantify the relationship between the offline simulation efforts and the online prediction accuracy. Particularly, we adopt measures of the maximal integrated mean squared error (IMSE) and integrated probability of false selection (IPFS) for assessing errors of the system performance and the best design predictions. Then, we establish convergence rates for the two measures under mild conditions. Last, these convergence behaviors are illustrated numerically using test examples.

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