Tinghan Ye, Sikai Cheng, Amira Hijazi, Pascal Van Hentenryck
The paper studies a large-scale order fulfillment problem for a leading e-commerce company in the United States. The challenge involves selecting fulfillment centers and shipping carriers with observational data only to efficiently process orders from a vast network of physical stores and warehouses. The company's current practice relies on heuristic rules that choose the cheapest fulfillment and shipping options for each unit, without considering opportunities for batching items or the reliability of carriers in meeting expected delivery dates. The paper develops a data-driven Contextual Stochastic Optimization (CSO) framework that integrates distributional forecasts of delivery time deviations with stochastic and robust order fulfillment optimization models. The framework optimizes the selection of fulfillment centers and carriers, accounting for item consolidation and delivery time uncertainty. Validated on a real-world data set containing tens of thousands of products, each with hundreds of fulfillment options, the proposed CSO framework significantly enhances the accuracy of meeting customer-expected delivery dates compared to current practices. It provides a flexible balance between reducing fulfillment costs and managing delivery time deviation risks, emphasizing the importance of contextual information and distributional forecasts in order fulfillment. This is the first paper that studies the omnichannel multi-courier order fulfillment problem with delivery time uncertainty through the lens of contextual optimization, fusing machine learning and optimization.
{"title":"Contextual Stochastic Optimization for Omnichannel Multi-Courier Order Fulfillment Under Delivery Time Uncertainty","authors":"Tinghan Ye, Sikai Cheng, Amira Hijazi, Pascal Van Hentenryck","doi":"arxiv-2409.06918","DOIUrl":"https://doi.org/arxiv-2409.06918","url":null,"abstract":"The paper studies a large-scale order fulfillment problem for a leading\u0000e-commerce company in the United States. The challenge involves selecting\u0000fulfillment centers and shipping carriers with observational data only to\u0000efficiently process orders from a vast network of physical stores and\u0000warehouses. The company's current practice relies on heuristic rules that\u0000choose the cheapest fulfillment and shipping options for each unit, without\u0000considering opportunities for batching items or the reliability of carriers in\u0000meeting expected delivery dates. The paper develops a data-driven Contextual\u0000Stochastic Optimization (CSO) framework that integrates distributional\u0000forecasts of delivery time deviations with stochastic and robust order\u0000fulfillment optimization models. The framework optimizes the selection of\u0000fulfillment centers and carriers, accounting for item consolidation and\u0000delivery time uncertainty. Validated on a real-world data set containing tens\u0000of thousands of products, each with hundreds of fulfillment options, the\u0000proposed CSO framework significantly enhances the accuracy of meeting\u0000customer-expected delivery dates compared to current practices. It provides a\u0000flexible balance between reducing fulfillment costs and managing delivery time\u0000deviation risks, emphasizing the importance of contextual information and\u0000distributional forecasts in order fulfillment. This is the first paper that\u0000studies the omnichannel multi-courier order fulfillment problem with delivery\u0000time uncertainty through the lens of contextual optimization, fusing machine\u0000learning and optimization.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper addresses a problem of sequential bilateral bargaining with incomplete information. We proposed a decision model that helps agents to successfully bargain by performing indirect negotiation and learning the opponent's model. Methodologically the paper casts heuristically-motivated bargaining of a self-interested independent player into a framework of Bayesian learning and Markov decision processes. The special form of the reward implicitly motivates the players to negotiate indirectly, via closed-loop interaction. We illustrate the approach by applying our model to the Nash demand game, which is an abstract model of bargaining. The results indicate that the established negotiation: i) leads to coordinating players' actions; ii) results in maximising success rate of the game and iii) brings more individual profit to the players.
{"title":"Indirect Dynamic Negotiation in the Nash Demand Game","authors":"Tatiana V. Guy, Jitka Homolová, Aleksej Gaj","doi":"arxiv-2409.06566","DOIUrl":"https://doi.org/arxiv-2409.06566","url":null,"abstract":"The paper addresses a problem of sequential bilateral bargaining with\u0000incomplete information. We proposed a decision model that helps agents to\u0000successfully bargain by performing indirect negotiation and learning the\u0000opponent's model. Methodologically the paper casts heuristically-motivated\u0000bargaining of a self-interested independent player into a framework of Bayesian\u0000learning and Markov decision processes. The special form of the reward\u0000implicitly motivates the players to negotiate indirectly, via closed-loop\u0000interaction. We illustrate the approach by applying our model to the Nash\u0000demand game, which is an abstract model of bargaining. The results indicate\u0000that the established negotiation: i) leads to coordinating players' actions;\u0000ii) results in maximising success rate of the game and iii) brings more\u0000individual profit to the players.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marta Baldomero-Naranjo, Ricardo Gázquez, Miguel Martínez-Antón, Luisa I. Martínez-Merino, Juan M. Muñoz-Ocaña, Francisco Temprano, Alberto Torrejón, Carlos Valverde, Nicolás Zerega
The topics of interest are location analysis and related problems. This includes location models, networks, transportation, logistics, exact and heuristic solution methods, and computational geometry, among many others.
{"title":"Proceedings of the XIII International Workshop on Locational Analysis and Related Problems","authors":"Marta Baldomero-Naranjo, Ricardo Gázquez, Miguel Martínez-Antón, Luisa I. Martínez-Merino, Juan M. Muñoz-Ocaña, Francisco Temprano, Alberto Torrejón, Carlos Valverde, Nicolás Zerega","doi":"arxiv-2409.06397","DOIUrl":"https://doi.org/arxiv-2409.06397","url":null,"abstract":"The topics of interest are location analysis and related problems. This\u0000includes location models, networks, transportation, logistics, exact and\u0000heuristic solution methods, and computational geometry, among many others.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Frederic MagoulesMICS, Mathieu MenouxMICS, Anna Rozanova-PierratMICS
In the framework of the optimal wave energy absorption, we solve theoretically and numerically a parametric shape optimization problem to find the optimal distribution of absorbing material in the reflexive one defined by a characteristic function in the Robin-type boundary condition associated with the Helmholtz equation. Robin boundary condition can be given on a part or the all boundary of a bounded ($epsilon$, $infty$)-domain of R n . The geometry of the partially absorbing boundary is fixed, but allowed to be non-Lipschitz, for example, fractal. It is defined as the support of a d-upper regular measure with d $in$]n -2, n[. Using the well-posedness properties of the model, for any fixed volume fraction of the absorbing material, we establish the existence of at least one optimal distribution minimizing the acoustical energy on a fixed frequency range of the relaxation problem. Thanks to the shape derivative of the energy functional, also existing for non-Lipschitz boundaries, we implement (in the two-dimensional case) the gradient descent method and find the optimal distribution with 50% of the absorbent material on a frequency range with better performances than the 100% absorbent boundary. The same type of performance is also obtained by the genetic method.
在最优波能吸收的框架下，我们从理论和数值上求解了一个参数形状优化问题，以找到吸收材料在与亥姆霍兹方程相关的罗宾型边界条件的特征函数所定义的反射一中的最优分布。罗宾边界条件可以在 R n 的有界（$epsilon$, $infty$）域的部分或全部边界上给出。部分吸收边界的几何形状是固定的，但允许是非 Lipschitz 的，例如分形。它被定义为具有 d $in$]n -2, n[ 的 d 上正则量的支持。利用该模型的好求解特性，对于任何固定体积分数的吸声材料，我们都能确定至少存在一种最优分布，能使松弛问题的固定频率范围内的声能最小化。由于能量函数的形状导数也存在于非 Lipschitz 边界，我们（在二维情况下）实施了梯度下降法，并在一个频率范围内找到了 50%吸声材料的最佳分布，其性能优于 100%吸声边界。遗传方法也获得了相同的性能。
{"title":"Frequency range non-Lipschitz parametric optimization of a noise absorption","authors":"Frederic MagoulesMICS, Mathieu MenouxMICS, Anna Rozanova-PierratMICS","doi":"arxiv-2409.06292","DOIUrl":"https://doi.org/arxiv-2409.06292","url":null,"abstract":"In the framework of the optimal wave energy absorption, we solve\u0000theoretically and numerically a parametric shape optimization problem to find\u0000the optimal distribution of absorbing material in the reflexive one defined by\u0000a characteristic function in the Robin-type boundary condition associated with\u0000the Helmholtz equation. Robin boundary condition can be given on a part or the\u0000all boundary of a bounded ($epsilon$, $infty$)-domain of R n . The geometry\u0000of the partially absorbing boundary is fixed, but allowed to be non-Lipschitz,\u0000for example, fractal. It is defined as the support of a d-upper regular measure\u0000with d $in$]n -2, n[. Using the well-posedness properties of the model, for\u0000any fixed volume fraction of the absorbing material, we establish the existence\u0000of at least one optimal distribution minimizing the acoustical energy on a\u0000fixed frequency range of the relaxation problem. Thanks to the shape derivative\u0000of the energy functional, also existing for non-Lipschitz boundaries, we\u0000implement (in the two-dimensional case) the gradient descent method and find\u0000the optimal distribution with 50% of the absorbent material on a frequency\u0000range with better performances than the 100% absorbent boundary. The same type\u0000of performance is also obtained by the genetic method.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce the KANtrol framework, which utilizes Kolmogorov-Arnold Networks (KANs) to solve optimal control problems involving continuous time variables. We explain how Gaussian quadrature can be employed to approximate the integral parts within the problem, particularly for integro-differential state equations. We also demonstrate how automatic differentiation is utilized to compute exact derivatives for integer-order dynamics, while for fractional derivatives of non-integer order, we employ matrix-vector product discretization within the KAN framework. We tackle multi-dimensional problems, including the optimal control of a 2D heat partial differential equation. The results of our simulations, which cover both forward and parameter identification problems, show that the KANtrol framework outperforms classical MLPs in terms of accuracy and efficiency.
本文介绍了 KANtrol 框架，该框架利用 Kolmogorov-Arnold 网络（KAN）来解决涉及连续时间变量的最优控制问题。我们解释了如何利用高斯正交来逼近问题中的积分部分，特别是对于积分微分状态方程。我们还演示了如何利用自动微分来计算整数阶动力学的精确导数，而对于非整数阶的分数导数，我们则在 KAN 框架内采用矩阵向量积离散化。我们解决了多维问题，包括二维热偏微分方程的优化控制。模拟结果表明，KAN 控制框架在精度和效率方面都优于经典 MLP。
{"title":"KANtrol: A Physics-Informed Kolmogorov-Arnold Network Framework for Solving Multi-Dimensional and Fractional Optimal Control Problems","authors":"Alireza Afzal Aghaei","doi":"arxiv-2409.06649","DOIUrl":"https://doi.org/arxiv-2409.06649","url":null,"abstract":"In this paper, we introduce the KANtrol framework, which utilizes\u0000Kolmogorov-Arnold Networks (KANs) to solve optimal control problems involving\u0000continuous time variables. We explain how Gaussian quadrature can be employed\u0000to approximate the integral parts within the problem, particularly for\u0000integro-differential state equations. We also demonstrate how automatic\u0000differentiation is utilized to compute exact derivatives for integer-order\u0000dynamics, while for fractional derivatives of non-integer order, we employ\u0000matrix-vector product discretization within the KAN framework. We tackle\u0000multi-dimensional problems, including the optimal control of a 2D heat partial\u0000differential equation. The results of our simulations, which cover both forward\u0000and parameter identification problems, show that the KANtrol framework\u0000outperforms classical MLPs in terms of accuracy and efficiency.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Arnaud Deza, Elias B. Khalil, Zhenan Fan, Zirui Zhou, Yong Zhang
We present $textit{Learn2Aggregate}$, a machine learning (ML) framework for optimizing the generation of Chv'atal-Gomory (CG) cuts in mixed integer linear programming (MILP). The framework trains a graph neural network to classify useful constraints for aggregation in CG cut generation. The ML-driven CG separator selectively focuses on a small set of impactful constraints, improving runtimes without compromising the strength of the generated cuts. Key to our approach is the formulation of a constraint classification task which favours sparse aggregation of constraints, consistent with empirical findings. This, in conjunction with a careful constraint labeling scheme and a hybrid of deep learning and feature engineering, results in enhanced CG cut generation across five diverse MILP benchmarks. On the largest test sets, our method closes roughly $textit{twice}$ as much of the integrality gap as the standard CG method while running 40$% faster. This performance improvement is due to our method eliminating 75% of the constraints prior to aggregation.
{"title":"Learn2Aggregate: Supervised Generation of Chvátal-Gomory Cuts Using Graph Neural Networks","authors":"Arnaud Deza, Elias B. Khalil, Zhenan Fan, Zirui Zhou, Yong Zhang","doi":"arxiv-2409.06559","DOIUrl":"https://doi.org/arxiv-2409.06559","url":null,"abstract":"We present $textit{Learn2Aggregate}$, a machine learning (ML) framework for\u0000optimizing the generation of Chv'atal-Gomory (CG) cuts in mixed integer linear\u0000programming (MILP). The framework trains a graph neural network to classify\u0000useful constraints for aggregation in CG cut generation. The ML-driven CG\u0000separator selectively focuses on a small set of impactful constraints,\u0000improving runtimes without compromising the strength of the generated cuts. Key\u0000to our approach is the formulation of a constraint classification task which\u0000favours sparse aggregation of constraints, consistent with empirical findings.\u0000This, in conjunction with a careful constraint labeling scheme and a hybrid of\u0000deep learning and feature engineering, results in enhanced CG cut generation\u0000across five diverse MILP benchmarks. On the largest test sets, our method\u0000closes roughly $textit{twice}$ as much of the integrality gap as the standard\u0000CG method while running 40$% faster. This performance improvement is due to our\u0000method eliminating 75% of the constraints prior to aggregation.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we illustrate the connection between adaptive mesh refinement for finite element discretized PDEs and the recently developed emph{bi-level regularization algorithm}. By adaptive mesh refinement according to data noise, regularization effect and convergence are immediate consequences. We moreover demonstrate its numerical advantages to the classical Landweber algorithm in term of time and reconstruction quality for the example of the Helmholtz equation in an aeroacoustic setting.
{"title":"Bi-level regularization via iterative mesh refinement for aeroacoustics","authors":"Christian Aarset, Tram Thi Ngoc Nguyen","doi":"arxiv-2409.06854","DOIUrl":"https://doi.org/arxiv-2409.06854","url":null,"abstract":"In this work, we illustrate the connection between adaptive mesh refinement\u0000for finite element discretized PDEs and the recently developed emph{bi-level\u0000regularization algorithm}. By adaptive mesh refinement according to data noise,\u0000regularization effect and convergence are immediate consequences. We moreover\u0000demonstrate its numerical advantages to the classical Landweber algorithm in\u0000term of time and reconstruction quality for the example of the Helmholtz\u0000equation in an aeroacoustic setting.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a policy iteration method to solve an inverse problem for a mean-field game model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the optimal costs for agents. The proposed approach decouples this complex inverse problem, which is an optimization problem constrained by a coupled nonlinear forward and backward PDE system in the MFG, into several iterations of solving linear PDEs and linear inverse problems. This method can also be viewed as a fixed-point iteration that simultaneously solves the MFG system and inversion. We further prove its linear rate of convergence. In addition, numerical examples in 1D and 2D, along with performance comparisons to a direct least-squares method, demonstrate the superior efficiency and accuracy of the proposed method for solving inverse MFGs.
{"title":"A Policy Iteration Method for Inverse Mean Field Games","authors":"Kui Ren, Nathan Soedjak, Shanyin Tong","doi":"arxiv-2409.06184","DOIUrl":"https://doi.org/arxiv-2409.06184","url":null,"abstract":"We propose a policy iteration method to solve an inverse problem for a\u0000mean-field game model, specifically to reconstruct the obstacle function in the\u0000game from the partial observation data of value functions, which represent the\u0000optimal costs for agents. The proposed approach decouples this complex inverse\u0000problem, which is an optimization problem constrained by a coupled nonlinear\u0000forward and backward PDE system in the MFG, into several iterations of solving\u0000linear PDEs and linear inverse problems. This method can also be viewed as a\u0000fixed-point iteration that simultaneously solves the MFG system and inversion.\u0000We further prove its linear rate of convergence. In addition, numerical\u0000examples in 1D and 2D, along with performance comparisons to a direct\u0000least-squares method, demonstrate the superior efficiency and accuracy of the\u0000proposed method for solving inverse MFGs.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sandra Zarychta, Marek Balcerzak, Katarzyna Wojdalska, Rafał Dolny, Jerzy Wojewoda
Pendulum-driven systems have emerged as a notable modification of vibro-impact mechanisms, replacing the conventional mass-on-spring oscillator with a pendulum. Such systems exhibit intricate behavior resulting from the interplay of directional dynamics, pendulum motion, and contact forces between the designed device and the underlying surface. This paper delves into the application of a Fourier series-based greedy algorithm for control optimization in pendulum capsule drives, which hold potential for diverse scenarios, including endoscopy capsule robots, pipeline inspection, and rescue operations in confined spaces. The emphasis is placed on experimental studies involving prototype development to validate the system's efficacy with previous computational simulations. Empirical findings closely align (<2% loss) with numerical investigations, showcasing the pendulum capsule drive's ability to achieve average speeds of 2.48 cm/s and 2.58 cm/s for three and six harmonics, respectively. These results are reinforced by high-quality signal-tracking accuracy, which demonstrates resilience against potential disturbances during motion. The authors envision the Fourier series-based control optimization method as a significant step towards ensuring enhanced locomotion performance in discontinuous systems, effectively handling the non-linearities arising from dry friction.
{"title":"Fourier series-based algorithm for control optimization in pendulum capsule drive: an integrated computational and experimental study","authors":"Sandra Zarychta, Marek Balcerzak, Katarzyna Wojdalska, Rafał Dolny, Jerzy Wojewoda","doi":"arxiv-2409.06824","DOIUrl":"https://doi.org/arxiv-2409.06824","url":null,"abstract":"Pendulum-driven systems have emerged as a notable modification of\u0000vibro-impact mechanisms, replacing the conventional mass-on-spring oscillator\u0000with a pendulum. Such systems exhibit intricate behavior resulting from the\u0000interplay of directional dynamics, pendulum motion, and contact forces between\u0000the designed device and the underlying surface. This paper delves into the\u0000application of a Fourier series-based greedy algorithm for control optimization\u0000in pendulum capsule drives, which hold potential for diverse scenarios,\u0000including endoscopy capsule robots, pipeline inspection, and rescue operations\u0000in confined spaces. The emphasis is placed on experimental studies involving\u0000prototype development to validate the system's efficacy with previous\u0000computational simulations. Empirical findings closely align (<2% loss) with\u0000numerical investigations, showcasing the pendulum capsule drive's ability to\u0000achieve average speeds of 2.48 cm/s and 2.58 cm/s for three and six harmonics,\u0000respectively. These results are reinforced by high-quality signal-tracking\u0000accuracy, which demonstrates resilience against potential disturbances during\u0000motion. The authors envision the Fourier series-based control optimization\u0000method as a significant step towards ensuring enhanced locomotion performance\u0000in discontinuous systems, effectively handling the non-linearities arising from\u0000dry friction.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper examines finite zero-sum stochastic games and demonstrates that when the game's duration is sufficiently long, there exists a pair of approximately optimal strategies such that the expected average payoff at any point in the game remains close to the value. This property, known as the textit{constant payoff property}, was previously established only for absorbing games and discounted stochastic games.
{"title":"Constant Payoff Property in Zero-Sum Stochastic Games with a Finite Horizon","authors":"Thomas Ragel, Bruno Ziliotto","doi":"arxiv-2409.05683","DOIUrl":"https://doi.org/arxiv-2409.05683","url":null,"abstract":"This paper examines finite zero-sum stochastic games and demonstrates that\u0000when the game's duration is sufficiently long, there exists a pair of\u0000approximately optimal strategies such that the expected average payoff at any\u0000point in the game remains close to the value. This property, known as the\u0000textit{constant payoff property}, was previously established only for\u0000absorbing games and discounted stochastic games.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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