Mathematics of Operations Research最新文献_第6页

Opinion Dynamics on Directed Complex Networks 有向复杂网络的舆论动力学

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-04-05 DOI: 10.1287/moor.2022.0250

Nicolas Fraiman, Tzu-Chi Lin, Mariana Olvera-Cravioto

引用次数: 0

Simple and Explicit Bounds for Multiserver Queues with 11−ρ Scaling 具有 11-ρ 缩放功能的多服务器队列的简单明确界限

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-04-02 DOI: 10.1287/moor.2022.0131

Yuan Li, David A. Goldberg

{"title":"Simple and Explicit Bounds for Multiserver Queues with 11−ρ Scaling","authors":"Yuan Li, David A. Goldberg","doi":"10.1287/moor.2022.0131","DOIUrl":"https://doi.org/10.1287/moor.2022.0131","url":null,"abstract":"We consider the first-come-first-serve (FCFS) [Formula: see text] queue and prove the first simple and explicit bounds that scale as [Formula: see text] under only the assumption that interarrival times have finite second moment, and service times have finite [Formula: see text] moment for some [Formula: see text]. Here, ρ denotes the corresponding traffic intensity. Conceptually, our results can be viewed as a multiserver analogue of Kingman’s bound. Our main results are bounds for the tail of the steady-state queue length and the steady-state probability of delay. The strength of our bounds (e.g., in the form of tail decay rate) is a function of how many moments of the service distribution are assumed finite. Our bounds scale gracefully, even when the number of servers grows large and the traffic intensity converges to unity simultaneously, as in the Halfin-Whitt scaling regime. Some of our bounds scale better than [Formula: see text] in certain asymptotic regimes. In these same asymptotic regimes, we also prove bounds for the tail of the steady-state number in service. Our main proofs proceed by explicitly analyzing the bounding process that arises in the stochastic comparison bounds of Gamarnik and Goldberg for multiserver queues. Along the way, we derive several novel results for suprema of random walks and pooled renewal processes, which may be of independent interest. We also prove several additional bounds using drift arguments (which have much smaller prefactors) and point out a conjecture that would imply further related bounds and generalizations. We also show that when all moments of the service distribution are finite and satisfy a mild growth rate assumption, our bounds can be strengthened to yield explicit tail estimates decaying as [Formula: see text], with [Formula: see text], depending on the growth rate of these moments.Funding: Financial support from the National Science Foundation [Grant 1333457] is gratefully acknowledged.Supplemental Material: The supplemental appendix is available at https://doi.org/10.1287/moor.2022.0131 .","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140582287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An Approximation to the Invariant Measure of the Limiting Diffusion of G/Ph/n + GI Queues in the Halfin–Whitt Regime and Related Asymptotics Halfin-Whitt 状态下 G/Ph/n + GI 队列极限扩散的不变量近似值及相关渐近线

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-29 DOI: 10.1287/moor.2021.0241

Xinghu Jin, Guodong Pang, Lihu Xu, Xin Xu

{"title":"An Approximation to the Invariant Measure of the Limiting Diffusion of G/Ph/n + GI Queues in the Halfin–Whitt Regime and Related Asymptotics","authors":"Xinghu Jin, Guodong Pang, Lihu Xu, Xin Xu","doi":"10.1287/moor.2021.0241","DOIUrl":"https://doi.org/10.1287/moor.2021.0241","url":null,"abstract":"In this paper, we develop a stochastic algorithm based on the Euler–Maruyama scheme to approximate the invariant measure of the limiting multidimensional diffusion of [Formula: see text] queues in the Halfin–Whitt regime. Specifically, we prove a nonasymptotic error bound between the invariant measures of the approximate model from the algorithm and the limiting diffusion. To establish the error bound, we employ the recently developed Stein’s method for multidimensional diffusions, in which the regularity of Stein’s equation obtained by the partial differential equation (PDE) theory plays a crucial role. We further prove the central limit theorem (CLT) and the moderate deviation principle (MDP) for the occupation measures of the limiting diffusion of [Formula: see text] queues and its Euler–Maruyama scheme. In particular, the variances in the CLT and MDP associated with the limiting diffusion are determined by Stein’s equation and Malliavin calculus, in which properties of a mollified diffusion and an associated weighted occupation time play a crucial role.Funding: X. Jin is supported in part by the Fundamental Research Funds for the Central Universities [Grants JZ2022HGQA0148 and JZ2023HGTA0170]. G. Pang is supported in part by the U.S. National Science Foundation [Grants DMS-1715875 and DMS-2216765]. L. Xu is supported in part by the National Nature Science Foundation of China [Grant 12071499], Macao Special Administrative Region [Grant FDCT 0090/2019/A2], and the University of Macau [Grant MYRG2018-00133-FST]. This work was supported by U.S. National Science Foundation [Grant DMS-2108683].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140582283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Sample-Path Large Deviations for Unbounded Additive Functionals of the Reflected Random Walk 反射随机漫步的无界加法函数的样本路径大偏差

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-27 DOI: 10.1287/moor.2020.0094

Mihail Bazhba, Jose Blanchet, Chang-Han Rhee, Bert Zwart

引用次数: 0

Steiner Cut Dominants 斯坦纳切割机

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-27 DOI: 10.1287/moor.2022.0280

Michele Conforti, Volker Kaibel

引用次数: 0

Uniqueness of Convex-Ranged Probabilities and Applications to Risk Measures and Games 凸范围概率的唯一性及其在风险度量和博弈中的应用

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-27 DOI: 10.1287/moor.2023.0015

M. Amarante, Felix-Benedikt Liebrich, Cosimo Munari

引用次数: 0

Exact Characterization of the Jointly Optimal Restocking and Auditing Policy in Inventory Systems with Record Inaccuracy 记录不准确的库存系统中联合最优补货和审计政策的精确特征描述

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-26 DOI: 10.1287/moor.2022.0145

Naveed Chehrazi

{"title":"Exact Characterization of the Jointly Optimal Restocking and Auditing Policy in Inventory Systems with Record Inaccuracy","authors":"Naveed Chehrazi","doi":"10.1287/moor.2022.0145","DOIUrl":"https://doi.org/10.1287/moor.2022.0145","url":null,"abstract":"We present a continuous-time stochastic model of an inventory system with record inaccuracy. In this formulation, demand is modeled by a point process and is observable only when it leads to sales. In addition to demand that can reduce the stock, an unobservable stochastic loss process can also reduce the stock. The retailer’s goal is to identify the restocking and auditing policy that minimizes the expected discounted cost of carrying a product over an infinite horizon. We analytically characterize the optimal restocking and jointly optimal auditing policy. We prove that the optimal restocking policy is a threshold policy. Our proof of this result is based on a coupling argument that is valid for any demand and loss model. Unlike the optimal restocking policy, the jointly optimal auditing policy is not of threshold type. We show that a complete proof of this statement cannot be obtained by solely resorting to the first-order stochastic dominance property of the Bayesian shelf stock distribution induced by the demand and loss process. Instead, our characterization of the jointly optimal auditing policy is based on proving that the dynamics of the shelf stock distribution constitute a (strictly) sign-regular kernel. To our knowledge, this is the first paper that characterizes the optimal policy of a complex control problem by establishing sign regularity of its underlying Markovian dynamics. Our theoretical results lead to a fast algorithm for computing the exact jointly optimal auditing/restocking policy over the problem’s entire state space. This enables comparative statics analysis, which allows us to determine how inventory record inaccuracy affects the economic significance of various cost drivers. This, in turn, allows us to determine when or, better, under what conditions auditing can be an effective tool for reducing the total cost.","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140381109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fast Rates for the Regret of Offline Reinforcement Learning 离线强化学习的快速回归率

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-25 DOI: 10.1287/moor.2021.0167

Yichun Hu, Nathan Kallus, Masatoshi Uehara

{"title":"Fast Rates for the Regret of Offline Reinforcement Learning","authors":"Yichun Hu, Nathan Kallus, Masatoshi Uehara","doi":"10.1287/moor.2021.0167","DOIUrl":"https://doi.org/10.1287/moor.2021.0167","url":null,"abstract":"We study the regret of offline reinforcement learning in an infinite-horizon discounted Markov decision process (MDP). While existing analyses of common approaches, such as fitted Q-iteration (FQI), suggest root-n convergence for regret, empirical behavior exhibits much faster convergence. In this paper, we present a finer regret analysis that exactly characterizes this phenomenon by providing fast rates for the regret convergence. First, we show that given any estimate for the optimal quality function, the regret of the policy it defines converges at a rate given by the exponentiation of the estimate’s pointwise convergence rate, thus speeding up the rate. The level of exponentiation depends on the level of noise in the decision-making problem, rather than the estimation problem. We establish such noise levels for linear and tabular MDPs as examples. Second, we provide new analyses of FQI and Bellman residual minimization to establish the correct pointwise convergence guarantees. As specific cases, our results imply one-over-n rates in linear cases and exponential-in-n rates in tabular cases. We extend our findings to general function approximation by extending our results to regret guarantees based on Lp-convergence rates for estimating the optimal quality function rather than pointwise rates, where L2 guarantees for nonparametric estimation can be ensured under mild conditions.Funding: This work was supported by the Division of Information and Intelligent Systems, National Science Foundation [Grant 1846210].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimal Investment Strategy for α-Robust Utility Maximization Problem α-稳健效用最大化问题的最优投资策略

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-21 DOI: 10.1287/moor.2023.0076

Zhou Yang, Danping Li, Yan Zeng, Guanting Liu

{"title":"Optimal Investment Strategy for α-Robust Utility Maximization Problem","authors":"Zhou Yang, Danping Li, Yan Zeng, Guanting Liu","doi":"10.1287/moor.2023.0076","DOIUrl":"https://doi.org/10.1287/moor.2023.0076","url":null,"abstract":"In reality, investors are uncertain about the dynamics of risky asset returns. Therefore, investors prefer to make robust investment decisions. In this paper, we propose an α-robust utility maximization problem under uncertain parameters. The investor is allowed to invest in a financial market consisting of a risk-free asset and a risky asset. The uncertainty about the expected return rate is parameterized by a nonempty set. Different from most existing literature on robust utility maximization problems where investors are generally assumed to be extremely ambiguity averse because they tend to consider only expected utility in the worst-case scenario, we pay attention to the investors who are not only ambiguity averse but also ambiguity seeking. Under power utility, we provide the implicit function representations for the precommitted strategy, equilibrium strategy of the open-loop type, and equilibrium strategy of the closed-loop type. Some properties about the optimal trading strategies, the best-case and worst-case parameters under three different kinds of strategies, are provided.Funding: This work was supported by National Natural Science Foundation of China [Grants 12071147, 12171169, 12271171, 12371470, 71721001, 71931004, 72371256], the Shanghai Philosophy Social Science Planning Office Project [Grant 2022ZJB005], Fundamental Research Funds for the Central Universities [Grant 2022QKT001], the Excellent Young Team Project Natural Science Foundation of Guangdong Province of China [Grant 2023B1515040001], the Philosophy and Social Science Programming Foundation of Guangdong Province [Grant GD22CYJ17], the Nature Science Foundation of Guangdong Province of China [Grant 2022A1515011472], and the 111 Project [Grant B14019].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140199553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Multilevel Langevin Pathwise Average for Gibbs Approximation 用于吉布斯逼近的多级朗之文路径平均法

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-03-20 DOI: 10.1287/moor.2021.0243

Maxime Egéa, Fabien Panloup

{"title":"Multilevel Langevin Pathwise Average for Gibbs Approximation","authors":"Maxime Egéa, Fabien Panloup","doi":"10.1287/moor.2021.0243","DOIUrl":"https://doi.org/10.1287/moor.2021.0243","url":null,"abstract":"We propose and study a new multilevel method for the numerical approximation of a Gibbs distribution π on [Formula: see text], based on (overdamped) Langevin diffusions. This method relies on a multilevel occupation measure, that is, on an appropriate combination of R occupation measures of (constant-step) Euler schemes with respective steps [Formula: see text]. We first state a quantitative result under general assumptions that guarantees an ε-approximation (in an L2-sense) with a cost of the order [Formula: see text] or [Formula: see text] under less contractive assumptions. We then apply it to overdamped Langevin diffusions with strongly convex potential [Formula: see text] and obtain an ε-complexity of the order [Formula: see text] or [Formula: see text] under additional assumptions on U. More precisely, up to universal constants, an appropriate choice of the parameters leads to a cost controlled by [Formula: see text] (where [Formula: see text] and [Formula: see text] respectively denote the supremum and the infimum of the largest and lowest eigenvalue of [Formula: see text]). We finally complete these theoretical results with some numerical illustrations, including comparisons to other algorithms in Bayesian learning and opening to the non–strongly convex setting.Funding: The authors are grateful to the SIRIC ILIAD Nantes-Angers program, supported by the French National Cancer Institute [INCA-DGOS-Inserm Grant 12558].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140297973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0