arXiv subjects

L. Jeff Hong

Publications and source records attributed to L. Jeff Hong.

At least 19 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.

math.OC↗

arXiv2025

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

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.

stat.ML↗

arXiv2025

UCB for Large-Scale Pure Exploration: Beyond Sub-Gaussianity

Selecting the best alternative from a finite set is the central objective of ranking and selection (R&S) and best arm identification (BAI). Traditional R&S or BAI approaches have predominantly relied on Gaussian or sub-Gaussian assumptions on the performance distributions of all alternatives, which limit their applicability to non-sub-Gaussian---especially heavy-tailed---problems. The need to move beyond sub-Gaussianity may become even more critical in large-scale problems, which tend to be especially sensitive to distributional specifications. In this paper, motivated by the widespread use of upper confidence bound (UCB) algorithms in sequential decision making, we investigate their performance in large-scale, non-sub-Gaussian R&S settings. We consider the simplest category of UCB algorithms, where the UCB value for each alternative is defined as the sample mean plus an exploration bonus that depends only on its own sample size. We abstract this into a meta-UCB algorithm and propose letting it select the alternative with the largest sample size as the best upon stopping. For this meta-UCB algorithm, we first derive a distribution-free lower bound on the probability of correct selection. Building on this bound, we first study the indifference-zone formulation and show that the meta-UCB algorithm---and therefore a broad class of UCB algorithms---achieves sample optimality as long as the variances are uniformly bounded. We then extend sample optimality to a non-indifference-zone configuration with polynomially shrinking mean gaps under the same variance assumption. These results demonstrate the applicability of UCB algorithms to large-scale R&S problems with non-sub-Gaussian distributions. Numerical experiments support our results and provide additional insights into the comparative behaviors of UCB algorithms within and beyond our meta-UCB framework.

stat.ML↗

arXiv2025

Sequential Additivity in Distributionally Robust Ranking and Selection

Ranking and selection (R&S) seeks to identify the alternative with the best mean performance from a finite collection of simulated alternatives. Its practical value depends on accurate simulation input modeling, which is often hindered by input uncertainty arising from limited data. Distributionally robust R&S (DRR&S) addresses this challenge by considering several plausible input distributions and selecting the alternative with the best worst-case mean performance, resulting in a multiplicative number of scenarios. Existing static and oracle analyses suggest that efficient sampling should instead be additive, concentrating on only a small number of critical scenarios. We introduce sequential additivity, which characterizes how this structure emerges from adaptive sequential procedures. We first establish an algorithm-independent sampling lower bound: any consistent DRR&S procedure must sample at least this additive number of scenarios infinitely often. We then study a simplified additive allocation (AA) procedure abstracted from practical sequential designs. Using boundary-crossing arguments, we derive a finite-budget upper bound on its probability of incorrect selection and show that this probability decays exponentially as the budget grows. Moreover, AA attains the necessary sampling lower bound exactly, showing that additivity can be achieved in the strongest possible sense. Surprisingly, the scenarios sampled infinitely often need not be the true worst-case scenarios, showing that worst-case scenario identification may not be necessary for sufficient exploration in DRR&S. To generalize these insights, we introduce a general additive allocation (GAA) framework that incorporates sampling rules from traditional R&S in a modular fashion. Under suitable exploration conditions, GAA procedures retain the key properties of AA.

stat.ML↗

arXiv2025

Conditional Generative Modeling for Enhanced Credit Risk Management in Supply Chain Finance

The rapid expansion of cross-border e-commerce (CBEC) has created significant opportunities for small- and medium-sized sellers, yet financing remains a critical challenge due to their limited credit histories. Third-party logistics (3PL)-led supply chain finance (SCF) has emerged as a promising solution, leveraging in-transit inventory as collateral. We propose an advanced credit risk management framework tailored for 3PL-led SCF, addressing the dual challenges of credit risk assessment and loan size determination. Specifically, we leverage conditional generative modeling of sales distributions through Quantile-Regression-based Generative Metamodeling (QRGMM) as the foundation for risk measures estimation. We propose a unified framework that enables flexible estimation of multiple risk measures while introducing a functional risk measure formulation that systematically captures the relationship between these risk measures and varying loan levels, supported by theoretical guarantees. To capture complex covariate interactions in e-commerce sales data, we integrate QRGMM with Deep Factorization Machines (DeepFM). Extensive experiments on synthetic and real-world data validate the efficacy of our model for credit risk assessment and loan size determination. This study explores the use of generative models in CBEC SCF risk management, illustrating their potential to strengthen credit assessment and support financing for small- and medium-sized sellers.

cs.LG↗

arXiv2025

LLMs for Supply Chain Management

The development of large language models (LLMs) has provided new tools for research in supply chain management (SCM). In this paper, we introduce a retrieval-augmented generation (RAG) framework that dynamically integrates external knowledge into the inference process, and develop a domain-specialized SCM LLM, which demonstrates expert-level competence by passing standardized SCM examinations and beer game tests. We further employ the use of LLMs to conduct horizontal and vertical supply chain games, in order to analyze competition and cooperation within supply chains. Our experiments show that RAG significantly improves performance on SCM tasks. Moreover, game-theoretic analysis reveals that the LLM can reproduce insights from the classical SCM literature, while also uncovering novel behaviors and offering fresh perspectives on phenomena such as the bullwhip effect. This paper opens the door for exploring cooperation and competition for complex supply chain network through the lens of LLMs.

cs.AI↗

arXiv2025

Efficient Budget Allocation for Large-Scale LLM-Enabled Virtual Screening

Screening tasks that aim to identify a small subset of top alternatives from a large pool are common in business decision-making processes. These tasks often require substantial human effort to evaluate each alternative's performance, making them time-consuming and costly. Motivated by recent advances in large language models (LLMs), particularly their ability to generate outputs that align well with human evaluations, we consider an LLM-as-human-evaluator approach for conducting screening virtually, thereby reducing the cost burden. To achieve scalability and cost-effectiveness in virtual screening, we identify that the stochastic nature of LLM outputs and their cost structure necessitate efficient budget allocation across all alternatives. To address this, we propose using a top-$m$ greedy evaluation mechanism, a simple yet effective approach that keeps evaluating the current top-$m$ alternatives, and design the explore-first top-$m$ greedy (EFG-$m$) algorithm. We prove that EFG-$m$ is both sample-optimal and consistent in large-scale virtual screening. Surprisingly, we also uncover a bonus ranking effect, where the algorithm naturally induces an indifference-based ranking within the selected subset. To further enhance practicality, we design a suite of algorithm variants to improve screening performance and computational efficiency. Numerical experiments validate our results and demonstrate the effectiveness of our algorithms. Lastly, we conduct a case study on LLM-based virtual screening. The study shows that while LLMs alone may not provide meaningful screening and ranking results when directly queried, integrating them with our sample-optimal algorithms unlocks their potential for cost-effective, large-scale virtual screening.

stat.ML↗

arXiv2025

New Additive OCBA Procedures for Robust Ranking and Selection

Robust ranking and selection (R&S) is an important and challenging variation of conventional R&S that seeks to select the best alternative among a finite set of alternatives. It captures the common input uncertainty in the simulation model by using an ambiguity set to include multiple possible input distributions and shifts to select the best alternative with the smallest worst-case mean performance over the ambiguity set. In this paper, we aim at developing new fixed-budget robust R&S procedures to minimize the probability of incorrect selection (PICS) under a limited sampling budget. Inspired by an additive upper bound of the PICS, we derive a new asymptotically optimal solution to the budget allocation problem. Accordingly, we design a new sequential optimal computing budget allocation (OCBA) procedure to solve robust R&S problems efficiently. We then conduct a comprehensive numerical study to verify the superiority of our robust OCBA procedure over existing ones. The numerical study also provides insights on the budget allocation behaviors that lead to enhanced efficiency.

stat.ME↗

arXiv2024

Efficient Nested Estimation of CoVaR: A Decoupled Approach

This paper addresses the estimation of the systemic risk measure known as CoVaR, which quantifies the risk of a financial portfolio conditional on another portfolio being at risk. We identify two principal challenges: conditioning on a zero-probability event and the repricing of portfolios. To tackle these issues, we propose a decoupled approach utilizing smoothing techniques and develop a model-independent theoretical framework grounded in a functional perspective. We demonstrate that the rate of convergence of the decoupled estimator can achieve approximately $O_{\rm P}(Γ^{-1/2})$, where $Γ$ represents the computational budget. Additionally, we establish the smoothness of the portfolio loss functions, highlighting its crucial role in enhancing sample efficiency. Our numerical results confirm the effectiveness of the decoupled estimators and provide practical insights for the selection of appropriate smoothing techniques.

q-fin.RM↗

arXiv2024

Review of Large-Scale Simulation Optimization

Large-scale simulation optimization (SO) problems encompass both large-scale ranking-and-selection problems and high-dimensional discrete or continuous SO problems, presenting significant challenges to existing SO theories and algorithms. This paper begins by providing illustrative examples that highlight the differences between large-scale SO problems and those of a more moderate scale. Subsequently, it reviews several widely employed techniques for addressing large-scale SO problems, such as divide and conquer, dimension reduction, and gradient-based algorithms. Additionally, the paper examines parallelization techniques leveraging widely accessible parallel computing environments to facilitate the resolution of large-scale SO problems.

math.OC↗

arXiv2024

Fast Discrete-Event Simulation of Markovian Queueing Networks through Euler Approximation

The efficient management of large-scale queueing networks is critical for a variety of sectors, including healthcare, logistics, and customer service, where system performance has profound implications for operational effectiveness and cost management. To address this key challenge, our paper introduces simulation techniques tailored for complex, large-scale Markovian queueing networks. We develop two simulation schemes based on Euler approximation, namely the backward and forward schemes. These schemes can accommodate time-varying dynamics and are optimized for efficient implementation using vectorization. Assuming a feedforward queueing network structure, we establish that the two schemes provide stochastic upper and lower bounds for the system state, while the approximation error remains bounded over the simulation horizon. With the recommended choice of time step, we show that our approximation schemes exhibit diminishing asymptotic relative error as the system scales up, while maintaining much lower computational complexity compared to traditional discrete-event simulation and achieving speedups up to tens of thousands times. This study highlights the substantial potential of Euler approximation in simulating large-scale discrete systems.

stat.ME↗

arXiv2024

AlphaRank: An Artificial Intelligence Approach for Ranking and Selection Problems

We introduce AlphaRank, an artificial intelligence approach to address the fixed-budget ranking and selection (R&S) problems. We formulate the sequential sampling decision as a Markov decision process and propose a Monte Carlo simulation-based rollout policy that utilizes classic R&S procedures as base policies for efficiently learning the value function of stochastic dynamic programming. We accelerate online sample-allocation by using deep reinforcement learning to pre-train a neural network model offline based on a given prior. We also propose a parallelizable computing framework for large-scale problems, effectively combining "divide and conquer" and "recursion" for enhanced scalability and efficiency. Numerical experiments demonstrate that the performance of AlphaRank is significantly improved over the base policies, which could be attributed to AlphaRank's superior capability on the trade-off among mean, variance, and induced correlation overlooked by many existing policies.

cs.LG↗

arXiv2023

The (Surprising) Sample Optimality of Greedy Procedures for Large-Scale Ranking and Selection

Ranking and selection (R&S) aims to select the best alternative with the largest mean performance from a finite set of alternatives. Recently, considerable attention has turned towards the large-scale R&S problem which involves a large number of alternatives. Ideal large-scale R&S procedures should be sample optimal, i.e., the total sample size required to deliver an asymptotically non-zero probability of correct selection (PCS) grows at the minimal order (linear order) in the number of alternatives, $k$. Surprisingly, we discover that the naïve greedy procedure, which keeps sampling the alternative with the largest running average, performs strikingly well and appears sample optimal. To understand this discovery, we develop a new boundary-crossing perspective and prove that the greedy procedure is sample optimal for the scenarios where the best mean maintains at least a positive constant away from all other means as $k$ increases. We further show that the derived PCS lower bound is asymptotically tight for the slippage configuration of means with a common variance. For other scenarios, we consider the probability of good selection and find that the result depends on the growth behavior of the number of good alternatives: if it remains bounded as $k$ increases, the sample optimality still holds; otherwise, the result may change. Moreover, we propose the explore-first greedy procedures by adding an exploration phase to the greedy procedure. The procedures are proven to be sample optimal and consistent under the same assumptions. Last, we numerically investigate the performance of our greedy procedures in solving large-scale R&S problems.

stat.ME↗

arXiv2023

Learning to Simulate: Generative Metamodeling via Quantile Regression

Stochastic simulation models effectively capture complex system dynamics but are often too slow for real-time decision-making. Traditional metamodeling techniques learn relationships between simulator inputs and a single output summary statistic, such as the mean or median. These techniques enable real-time predictions without additional simulations. However, they require prior selection of one appropriate output summary statistic, limiting their flexibility in practical applications. We propose a new concept: generative metamodeling. It aims to construct a "fast simulator of the simulator," generating random outputs significantly faster than the original simulator while preserving approximately equal conditional distributions. Generative metamodels enable rapid generation of numerous random outputs upon input specification, facilitating immediate computation of any summary statistic for real-time decision-making. We introduce a new algorithm, quantile-regression-based generative metamodeling (QRGMM), and establish its distributional convergence and convergence rate. Extensive numerical experiments demonstrate QRGMM's efficacy compared to other state-of-the-art generative algorithms in practical real-time decision-making scenarios.

cs.LG↗

arXiv2023

Staffing under Taylor's Law: A Unifying Framework for Bridging Square-root and Linear Safety Rules

Staffing rules are an essential management tool in service industries for meeting target service levels. The square-root safety rule, based on the Poisson arrival assumption, has been commonly used. However, empirical findings suggest that arrivals often exhibit ``over-dispersion'', meaning that the variance exceeds the mean. In this paper, we develop a new doubly stochastic Poisson process model that captures two key features of over-dispersed arrivals: (i) Taylor's law, which links the variance to the mean through a power-law relationship, and (ii) temporal correlation decay, where the correlation between arrival counts in disjoint time intervals decreases as the time gap grows. Using this model, we study how over-dispersion affects staffing and derive a closed-form staffing formula to ensure a desired service level. Our formula shows that the safety level grows as a power of the nominal load. The exponent lies between 1/2 (the square-root safety rule) and 1 (the linear safety rule). It depends on the degree of over-dispersion, and it implies that Taylor's law is the dominant factor in determining staffing levels in heavy traffic. Extensive numerical experiments with both simulated and real arrival data show that our model and staffing rules significantly outperform various alternatives.

math.PR↗

arXiv2022

Monte-Carlo Estimation of CoVaR

${\rm CoVaR}$ is one of the most important measures of financial systemic risks. It is defined as the risk of a financial portfolio conditional on another financial portfolio being at risk. In this paper we first develop a Monte-Carlo simulation-based batching estimator of CoVaR and study its consistency and asymptotic normality. We show that the optimal rate of convergence of the batching estimator is $n^{-1/3}$, where $n$ is the sample size. We then develop an importance-sampling inspired estimator under the delta-gamma approximations to the portfolio losses, and we show that the rate of convergence of the estimator is $n^{-1/2}$. Numerical experiments support our theoretical findings and show that both estimators work well.

q-fin.RM↗

arXiv2022

A Dimension-free Algorithm for Contextual Continuum-armed Bandits

In contextual continuum-armed bandits, the contexts $x$ and the arms $y$ are both continuous and drawn from high-dimensional spaces. The payoff function to learn $f(x,y)$ does not have a particular parametric form. The literature has shown that for Lipschitz-continuous functions, the optimal regret is $\tilde{O}(T^{\frac{d_x+d_y+1}{d_x+d_y+2}})$, where $d_x$ and $d_y$ are the dimensions of contexts and arms, and thus suffers from the curse of dimensionality. We develop an algorithm that achieves regret $\tilde{O}(T^{\frac{d_x+1}{d_x+2}})$ when $f$ is globally concave in $y$. The global concavity is a common assumption in many applications. The algorithm is based on stochastic approximation and estimates the gradient information in an online fashion. Our results generate a valuable insight that the curse of dimensionality of the arms can be overcome with some mild structures of the payoff function.

stat.ML↗

arXiv2022

Dimension Reduction in Contextual Online Learning via Nonparametric Variable Selection

We consider a contextual online learning (multi-armed bandit) problem with high-dimensional covariate $\mathbf{x}$ and decision $\mathbf{y}$. The reward function to learn, $f(\mathbf{x},\mathbf{y})$, does not have a particular parametric form. The literature has shown that the optimal regret is $\tilde{O}(T^{(d_x+d_y+1)/(d_x+d_y+2)})$, where $d_x$ and $d_y$ are the dimensions of $\mathbf x$ and $\mathbf y$, and thus it suffers from the curse of dimensionality. In many applications, only a small subset of variables in the covariate affect the value of $f$, which is referred to as \textit{sparsity} in statistics. To take advantage of the sparsity structure of the covariate, we propose a variable selection algorithm called \textit{BV-LASSO}, which incorporates novel ideas such as binning and voting to apply LASSO to nonparametric settings. Our algorithm achieves the regret $\tilde{O}(T^{(d_x^*+d_y+1)/(d_x^*+d_y+2)})$, where $d_x^*$ is the effective covariate dimension. The regret matches the optimal regret when the covariate is $d^*_x$-dimensional and thus cannot be improved. Our algorithm may serve as a general recipe to achieve dimension reduction via variable selection in nonparametric settings.

cs.LG↗