arXiv subjects

Yanyuan Wang

Publications and source records attributed to Yanyuan Wang.

3 recordsLinked to original sources

arXiv2026

Optimizing Service Operations via LLM-Powered Multi-Agent Simulation

Service system performance depends on how participants respond to design choices, but modeling these responses is hard due to the complexity of human behavior. We introduce an LLM-powered multi-agent simulation (LLM-MAS) framework for optimizing service operations. We pose the problem as stochastic optimization with decision-dependent uncertainty: design choices are embedded in prompts and shape the distribution of outcomes from interacting LLM-powered agents. By embedding key numerical information in prompts and extracting it from LLM-generated text, we model this uncertainty as a controlled Markov chain. We develop an on-trajectory learning algorithm that, on a single simulation run, simultaneously constructs zeroth-order gradient estimates and updates design parameters to optimize steady-state performance. We also incorporate variance reduction techniques. In a sustainable supply chain application, our method outperforms benchmarks, including blackbox optimization and using LLMs as numerical solvers or as role-playing system designers. A case study on optimal contest design with real behavioral data shows that LLM-MAS is both as a cost-effective evaluator of known designs and an exploratory tool that can uncover strong designs overlooked by traditional approaches.

cs.AI↗

arXiv2025

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

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.

math.OC↗

arXiv2023

Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensions

Nested simulation concerns estimating functionals of a conditional expectation via simulation. In this paper, we propose a new method based on kernel ridge regression to exploit the smoothness of the conditional expectation as a function of the multidimensional conditioning variable. Asymptotic analysis shows that the proposed method can effectively alleviate the curse of dimensionality on the convergence rate as the simulation budget increases, provided that the conditional expectation is sufficiently smooth. The smoothness bridges the gap between the cubic root convergence rate (that is, the optimal rate for the standard nested simulation) and the square root convergence rate (that is, the canonical rate for the standard Monte Carlo simulation). We demonstrate the performance of the proposed method via numerical examples from portfolio risk management and input uncertainty quantification.

stat.ME↗