Mathematics of Operations Research

最新文章

• Linear Mean-Field Games with Discounted Cost AI翻译
  作者：Saldi, Naci
  作者单位：Ihsan Dogramaci Bilkent University
  摘要：In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. At every time, each agent is randomly coupled with another agent via their dynamics and one-stage cost function, where this randomization is generated via the empirical distribution of their states (i.e., the mean-field term). Therefore, the transition probability and the one-stage cost function of each agent depend linearly on the mean-field term, which is the...
• Optimal Partition for a Multi-Type Queueing System AI翻译
  作者：Cao, Shengyu; He, Simai; Wang, Zizhuo; Feng, Yifan
  作者单位：University of Toronto; Shanghai Jiao Tong University; The Chinese University of Hong Kong, Shenzhen; National University of Singapore
  摘要：We study an optimal server partition and customer assignment problem for an uncapacitated first-come-first-served queueing system with heterogeneous types of customers. Each type of customer is associated with a Poisson arrival, a certain service time distribution, and a unit waiting cost. The goal is to minimize the expected total waiting cost by partitioning the server into subqueues, each with a smaller service capacity, and routing customer types probabilistically. First, we show that by p...
• Robust Multiple Stopping-A Duality Approach AI翻译
  作者：Laeven, Roger J. A.; Schoenmakers, John G. M.; Schweizer, Nikolaus; Stadje, Mitja
  作者单位：University of Amsterdam; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Tilburg University; Ulm University; Ulm University
  摘要：We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights-that is, optimal multiple stopping-for a robust evaluation that accounts for model uncertainty with a dominated family of priors and for general reward processes driven by multidimensional jump-diffusions. Our approach relies on first establishing robust martingale dual representation results for the multiple stopping problem that satisfy appea...
• A Policy Gradient Algorithm for the Risk-Sensitive Exponential Cost MDP AI翻译
  作者：Moharrami, Mehrdad; Murthy, Yashaswini; Roy, Arghyadip; Srikant, R.
  作者单位：University of Iowa; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Guwahati
  摘要：We study the risk -sensitive exponential cost Markov decision process (MDP) formulation and develop a trajectory -based gradient algorithm to find the stationary point of the cost associated with a set of parameterized policies. We derive a formula that can be used to compute the policy gradient from (state, action, cost) information collected from sample paths of the MDP for each fixed parameterized policy. Unlike the traditional average cost problem, standard stochastic approximation theory ...
• Dual Solutions in Convex Stochastic Optimization AI翻译
  作者：Pennanen, Teemu; Perkkioe, Ari-Pekka
  作者单位：University of London; King's College London; University of Munich
  摘要：This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex space of random variables. It implies, in particular, the necessity of scenario-wise optimality conditions that are behind many fundamental results in operations research, stochastic optimal control, and financial mathematics. Our analysis builds on the theor...
• Robust Online Selection with Uncertain Offer Acceptance AI翻译
  作者：Perez-Salazar, Sebastian; Singh, Mohit; Toriello, Alejandro
  作者单位：Rice University; University System of Georgia; Georgia Institute of Technology
  摘要：Online advertising has motivated interest in online selection problems. Displaying ads to the right users benefits both the platform (e.g., via pay-per-click) and the advertisers (by increasing their reach). In practice, not all users click on displayed ads, while the platform's algorithm may miss the users most disposed to do so. This mismatch decreases the platform's revenue and the advertiser's chances to reach the right customers. With this motivation, we propose a secretary problem where ...
• A Moment-Sum-of-Squares Hierarchy for Robust Polynomial Matrix Inequality Optimization with Sum-of-Squares Convexity AI翻译
  作者：Guo, Feng; Wang, Jie
  作者单位：Dalian University of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
  摘要：We study a class of polynomial optimization problems with a robust polynomial matrix inequality (PMI) constraint where the uncertainty set itself is also defined by a PMI. These can be viewed as matrix generalizations of semi-infinite polynomial programs because they involve actually infinitely many PMI constraints in general. Under certain sum-of-squares (SOS)-convexity assumptions, we construct a hierarchy of increasingly tight moment-SOS relaxations for solving such problems. Most of the ni...
• Optimality Conditions in Control Problems with Random State Constraints in Probabilistic or Almost Sure Form AI翻译
  作者：Geiersbach, Caroline; Henrion, Rene
  作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
  摘要：In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. Although the latter can be understood as the limiting case of the former, the derivation of optimality conditions requires substantially different approaches. We apply them to a linear elliptic partial differential equation with random inputs. In the probabilistic case, we rely on the spherical-radial decomposition of Gaussian ran...
• Markov Decision Processes with Observation Costs: Framework and Computation with a Penalty Scheme AI翻译
  作者：Reisinger, Christoph; Tam, Jonathan
  作者单位：University of Oxford
  摘要：We consider Markov decision processes where the state of the chain is only given at chosen observation times and of a cost. Optimal strategies involve the optimization of observation times as well as the subsequent action values. We consider the finite horizon and discounted infinite horizon problems as well as an extension with parameter uncertainty. By including the time elapsed from observations as part of the augmented Markov system, the value function satisfies a system of quasivariationa...
• Estimating a Function and Its Derivatives Under a Smoothness Condition AI翻译
  作者：Lim, Eunji
  作者单位：Adelphi University
  摘要：We consider the problem of estimating an unknown function f & lowast; : Rd d -> R and its partial derivatives from a noisy data set of n observations, where we make no assumptions about f & lowast; except that it is smooth in the sense that it has square integrable partial derivatives of order m . A natural candidate for the estimator of f & lowast; in such a case is the best fit to the data set that satisfies a certain smoothness condition. This estimator can be seen as a least squares estima...